AP Precalculus Flashcards: Composition Of Functions

Study Composition Of Functions in AP Precalculus with focused flashcards that help you recognize the idea, recall the key rule, and apply it in practice-style prompts.

AP Precalculus

Composition Of Functions

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QUESTION

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Find $(g \bigcirc f)(x)$ if $f(x) = x + 2$ and $g(x) = 3x$ .

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ANSWER

$(g \bigcirc f)(x) = 3(x + 2)$ . Apply $g$ to $f(x) = x + 2$ : $3(x + 2)$ .

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This deck focuses on Composition Of Functions, giving you a quick way to review the definitions, rules, and examples that matter most for AP Precalculus.

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Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

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Flashcard 1: Find $(g \bigcirc f)(x)$ if $f(x) = x + 2$ and $g(x) = 3x$ .

Answer: $(g \bigcirc f)(x) = 3(x + 2)$ . Apply $g$ to $f(x) = x + 2$ : $3(x + 2)$ .

Flashcard 2: What is the definition of the composition of functions?

Answer: It is applying one function to the results of another: $(f \bigcirc g)(x) = f(g(x))$ . First apply g, then apply f to that result.

Flashcard 3: What is the definition of the composition of functions?

Answer: It is applying one function to the results of another: $(f \bigcirc g)(x) = f(g(x))$ . First apply g, then apply f to that result.

Flashcard 4: If $f(x) = x - 3$ and $g(x) = x^2$ , find $(f \bigcirc g)(x)$ .

Answer: $(f \bigcirc g)(x) = x^2 - 3$ . Apply $f$ to $g(x) = x^2$ : $x^2 - 3$ .

Flashcard 5: If $f(x) = 2x$ and $g(x) = x + 3$ , what is $(f \bigcirc g)(x)$ ?

Answer: $(f \bigcirc g)(x) = 2(x + 3)$ . Substitute $g(x) = x + 3$ into $f$ .

Flashcard 6: Find $(f \bigcirc g)(x)$ if $f(x) = x^2 + 1$ and $g(x) = 3x$ .

Answer: $(f \bigcirc g)(x) = 9x^2 + 1$ . Substitute $g(x) = 3x$ into $f$ : $(3x)^2 + 1$ .

Flashcard 7: Find $(g \bigcirc f)(x)$ if $f(x) = x^2$ and $g(x) = \frac{1}{x}$ .

Answer: $(g \bigcirc f)(x) = \frac{1}{x^2}$ . Apply $g$ to $f(x) = x^2$ : $\frac{1}{x^2}$ .

Flashcard 8: What is $(g \bigcirc f)(5)$ for $f(x) = 3x$ and $g(x) = x - 2$ ?

Answer: $(g \bigcirc f)(5) = 13$ . $f(5) = 15$ , then $g(15) = 13$ .

Flashcard 9: If $f(x) = x^2$ and $g(x) = x + 1$ , what is $(f \bigcirc g)(1)$ ?

Answer: $(f \bigcirc g)(1) = 4$ . $g(1) = 2$ , then $f(2) = 4$ .

Flashcard 10: What is $(f \bigcirc g)(0)$ for $f(x) = 2x + 3$ and $g(x) = x^2$ ?

Answer: $(f \bigcirc g)(0) = 3$ . $g(0) = 0$ , then $f(0) = 3$ .

Flashcard 11: If $f(x) = x^2$ and $g(x) = 3x + 1$ , find $(g \bigcirc f)(x)$ .

Answer: $(g \bigcirc f)(x) = 3x^2 + 1$ . Apply $g$ to $f(x) = x^2$ : $g(x^2) = 3x^2 + 1$ .

Flashcard 12: What is $(g \bigcirc f)(x)$ for $f(x) = \frac{1}{x}$ and $g(x) = x^2$ ?

Answer: $(g \bigcirc f)(x) = \frac{1}{x^2}$ . Apply $g$ to $f(x) = \frac{1}{x}$ : $(\frac{1}{x})^2$ .

Flashcard 13: If $f(x) = 4x$ and $g(x) = x - 2$ , find $(f \bigcirc g)(x)$ .

Answer: $(f \bigcirc g)(x) = 4(x - 2)$ . Apply $f$ to $g(x) = x - 2$ : $4(x - 2)$ .

Flashcard 14: What is $(f \bigcirc g)(x)$ for $f(x) = x^3$ and $g(x) = \frac{1}{x}$ ?

Answer: $(f \bigcirc g)(x) = \frac{1}{x^3}$ . Apply $f$ to $g(x) = \frac{1}{x}$ : $(\frac{1}{x})^3$ .

Flashcard 15: If $f(x) = 4x$ and $g(x) = x - 2$ , find $(f \bigcirc g)(x)$ .

Answer: $(f \bigcirc g)(x) = 4(x - 2)$ . Apply $f$ to $g(x) = x - 2$ : $4(x - 2)$ .

Flashcard 16: If $f(x) = \frac{1}{x}$ and $g(x) = x + 2$ , find $(f \bigcirc g)(x)$ .

Answer: $(f \bigcirc g)(x) = \frac{1}{x + 2}$ . Apply $f$ to $g(x) = x + 2$ : $\frac{1}{x + 2}$ .

Flashcard 17: Determine $(f \bigcirc g)(x)$ if $f(x) = 1/x$ and $g(x) = x - 5$ .

Answer: $(f \bigcirc g)(x) = 1/(x - 5)$ . Apply $f$ to the result $g(x) = x - 5$ .

Flashcard 18: What is $(f \bigcirc g)(2)$ if $f(x) = 3x$ and $g(x) = x - 1$ ?

Answer: $(f \bigcirc g)(2) = 3$ . $g(2) = 1$ , then $f(1) = 3$ .

Flashcard 19: Write $(f \bigcirc g)(x)$ for $f(x) = x^3$ and $g(x) = \frac{1}{x}$ .

Answer: $(f \bigcirc g)(x) = (1/x)^3$ . Substitute $g(x) = \frac{1}{x}$ into $f(x) = x^3$ .

Flashcard 20: Determine $(g \bigcirc f)(x)$ if $f(x) = x + 1$ and $g(x) = x^3$ .

Answer: $(g \bigcirc f)(x) = (x + 1)^3$ . Apply $g$ to $f(x) = x + 1$ : $(x + 1)^3$ .

Flashcard 21: If $f(x) = x - 3$ and $g(x) = x^2$ , find $(f \bigcirc g)(x)$ .

Answer: $(f \bigcirc g)(x) = x^2 - 3$ . Apply $f$ to $g(x) = x^2$ : $x^2 - 3$ .

Flashcard 22: Calculate $(f \bigcirc g)(x)$ if $f(x) = 2x + 1$ and $g(x) = x^3$ .

Answer: $(f \bigcirc g)(x) = 2x^3 + 1$ . Apply $f$ to $g(x) = x^3$ : $2x^3 + 1$ .

Flashcard 23: If $f(x) = x^2$ and $g(x) = x + 2$ , find $(g \bigcirc f)(x)$ .

Answer: $(g \bigcirc f)(x) = x^2 + 2$ . Apply $g$ to $f(x) = x^2$ : $x^2 + 2$ .

Flashcard 24: If $f(x) = 2x + 1$ and $g(x) = x - 3$ , find $(f \bigcirc g)(x)$ .

Answer: $(f \bigcirc g)(x) = 2(x - 3) + 1$ . Substitute $g(x) = x - 3$ into $f$ .

Flashcard 25: Find $(f \bigcirc g)(-1)$ if $f(x) = x^2$ and $g(x) = x + 5$ .

Answer: $(f \bigcirc g)(-1) = 16$ . $g(-1) = 4$ , then $f(4) = 16$ .

Flashcard 26: If $f(x) = x^2$ and $g(x) = x + 1$ , what is $(f \bigcirc g)(1)$ ?

Answer: $(f \bigcirc g)(1) = 4$ . $g(1) = 2$ , then $f(2) = 4$ .

Flashcard 27: Find $(g \bigcirc f)(0)$ for $f(x) = x^2 + 1$ and $g(x) = 2x$ .

Answer: $(g \bigcirc f)(0) = 2$ . $f(0) = 1$ , then $g(1) = 2$ .

Flashcard 28: Determine $(f \bigcirc g)(x)$ for $f(x) = x^2$ and $g(x) = x + 1$ .

Answer: $(f \bigcirc g)(x) = (x + 1)^2$ . Apply $f$ to $g(x) = x + 1$ : $(x + 1)^2$ .

Flashcard 29: If $f(x) = 5x$ and $g(x) = x - 3$ , find $(f \bigcirc g)(x)$ .

Answer: $(f \bigcirc g)(x) = 5(x - 3)$ . Substitute $g(x) = x - 3$ into $f(x) = 5x$ .

Flashcard 30: Determine $(f \bigcirc g)(1)$ if $f(x) = x - 2$ and $g(x) = x^2$ .

Answer: $(f \bigcirc g)(1) = -1$ . $g(1) = 1$ , then $f(1) = -1$ .

Flashcard 31: What is $(f \bigcirc g)(x)$ for $f(x) = x^3$ and $g(x) = \frac{1}{x}$ ?

Answer: $(f \bigcirc g)(x) = \frac{1}{x^3}$ . Apply $f$ to $g(x) = \frac{1}{x}$ : $(\frac{1}{x})^3$ .

Flashcard 32: If $f(x) = 5x$ and $g(x) = x - 3$ , find $(f \bigcirc g)(x)$ .

Answer: $(f \bigcirc g)(x) = 5(x - 3)$ . Substitute $g(x) = x - 3$ into $f(x) = 5x$ .

Flashcard 33: If $f(x) = \frac{1}{x}$ and $g(x) = x + 2$ , find $(f \bigcirc g)(x)$ .

Answer: $(f \bigcirc g)(x) = \frac{1}{x + 2}$ . Apply $f$ to $g(x) = x + 2$ : $\frac{1}{x + 2}$ .

Flashcard 34: Write $(f \bigcirc g)(x)$ for $f(x) = x^3$ and $g(x) = \frac{1}{x}$ .

Answer: $(f \bigcirc g)(x) = (1/x)^3$ . Substitute $g(x) = \frac{1}{x}$ into $f(x) = x^3$ .

Flashcard 35: What is $(g \bigcirc f)(5)$ for $f(x) = 3x$ and $g(x) = x - 2$ ?

Answer: $(g \bigcirc f)(5) = 13$ . $f(5) = 15$ , then $g(15) = 13$ .

Flashcard 36: If $f(x) = x^2$ and $g(x) = x + 2$ , find $(g \bigcirc f)(x)$ .

Answer: $(g \bigcirc f)(x) = x^2 + 2$ . Apply $g$ to $f(x) = x^2$ : $x^2 + 2$ .

Flashcard 37: If $f(x) = 2x + 3$ , find $(f \bigcirc f)(x)$ .

Answer: $(f \bigcirc f)(x) = 2(2x + 3) + 3$ . Substitute $f(x)$ into itself.

Flashcard 38: If $f(x) = x^2 + 2$ and $g(x) = 4x$ , find $(f \bigcirc g)(x)$ .

Answer: $(f \bigcirc g)(x) = 16x^2 + 2$ . Substitute $g(x) = 4x$ into $f$ : $(4x)^2 + 2$ .

Flashcard 39: Find $(g \bigcirc f)(x)$ if $f(x) = x + 2$ and $g(x) = 3x$ .

Answer: $(g \bigcirc f)(x) = 3(x + 2)$ . Apply $g$ to $f(x) = x + 2$ : $3(x + 2)$ .

Flashcard 40: Find $(f \bigcirc g)(x)$ if $f(x) = x^2 + 1$ and $g(x) = 3x$ .

Answer: $(f \bigcirc g)(x) = 9x^2 + 1$ . Substitute $g(x) = 3x$ into $f$ : $(3x)^2 + 1$ .

Flashcard 41: Find $(f \bigcirc g)(-1)$ if $f(x) = x^2$ and $g(x) = x + 5$ .

Answer: $(f \bigcirc g)(-1) = 16$ . $g(-1) = 4$ , then $f(4) = 16$ .

Flashcard 42: If $f(x) = x^2 + 2$ and $g(x) = 4x$ , find $(f \bigcirc g)(x)$ .

Answer: $(f \bigcirc g)(x) = 16x^2 + 2$ . Substitute $g(x) = 4x$ into $f$ : $(4x)^2 + 2$ .

Flashcard 43: What is $(f \bigcirc g)(0)$ for $f(x) = 2x + 3$ and $g(x) = x^2$ ?

Answer: $(f \bigcirc g)(0) = 3$ . $g(0) = 0$ , then $f(0) = 3$ .

Flashcard 44: Calculate $(g \bigcirc f)(3)$ for $f(x) = 2x$ and $g(x) = x^2$ .

Answer: $(g \bigcirc f)(3) = 36$ . $f(3) = 6$ , then $g(6) = 36$ .

Flashcard 45: What is $(f \bigcirc g)(x)$ for $f(x) = \frac{1}{2}x$ and $g(x) = x + 4$ ?

Answer: $(f \bigcirc g)(x) = \frac{1}{2}(x + 4)$ . Apply $f$ to $g(x) = x + 4$ .

Flashcard 46: Calculate $(g \bigcirc f)(-3)$ for $f(x) = 3x + 1$ and $g(x) = x^2$ .

Answer: $(g \bigcirc f)(-3) = 64$ . $f(-3) = -8$ , then $g(-8) = 64$ .

Flashcard 47: Find $(g \bigcirc f)(0)$ for $f(x) = x^2 + 1$ and $g(x) = 2x$ .

Answer: $(g \bigcirc f)(0) = 2$ . $f(0) = 1$ , then $g(1) = 2$ .

Flashcard 48: Determine $(f \bigcirc g)(x)$ if $f(x) = 1/x$ and $g(x) = x - 5$ .

Answer: $(f \bigcirc g)(x) = 1/(x - 5)$ . Apply $f$ to the result $g(x) = x - 5$ .

Flashcard 49: Evaluate $(g \bigcirc f)(2)$ if $f(x) = x + 1$ and $g(x) = 2x$ .

Answer: $(g \bigcirc f)(2) = 6$ . $f(2) = 3$ , then $g(3) = 6$ .

Flashcard 50: State the notation for composing functions $f(x)$ and $g(x)$ .

Answer: $(f \bigcirc g)(x) = f(g(x))$ . Standard notation for function composition.

Flashcard 51: If $f(x) = 2x + 3$ , find $(f \bigcirc f)(x)$ .

Answer: $(f \bigcirc f)(x) = 2(2x + 3) + 3$ . Substitute $f(x)$ into itself.

Flashcard 52: If $f(x) = x - 4$ and $g(x) = x^2$ , find $(f \bigcirc g)(x)$ .

Answer: $(f \bigcirc g)(x) = x^2 - 4$ . Apply $f$ to $g(x) = x^2$ : $x^2 - 4$ .

Flashcard 53: If $f(x) = x + 1$ and $g(x) = x^2$ , what is $(f \bigcirc g)(-2)$ ?

Answer: $(f \bigcirc g)(-2) = 5$ . $g(-2) = 4$ , then $f(4) = 5$ .

Flashcard 54: Determine $(f \bigcirc g)(x)$ for $f(x) = x^2$ and $g(x) = x + 1$ .

Answer: $(f \bigcirc g)(x) = (x + 1)^2$ . Apply $f$ to $g(x) = x + 1$ : $(x + 1)^2$ .

Flashcard 55: Determine $(f \bigcirc g)(1)$ if $f(x) = x - 2$ and $g(x) = x^2$ .

Answer: $(f \bigcirc g)(1) = -1$ . $g(1) = 1$ , then $f(1) = -1$ .

Flashcard 56: Evaluate $(g \bigcirc f)(2)$ if $f(x) = x + 1$ and $g(x) = 2x$ .

Answer: $(g \bigcirc f)(2) = 6$ . $f(2) = 3$ , then $g(3) = 6$ .

Flashcard 57: If $f(x) = 2x$ and $g(x) = x + 3$ , what is $(f \bigcirc g)(x)$ ?

Answer: $(f \bigcirc g)(x) = 2(x + 3)$ . Substitute $g(x) = x + 3$ into $f$ .

Flashcard 58: Calculate $(g \bigcirc f)(3)$ for $f(x) = 2x$ and $g(x) = x^2$ .

Answer: $(g \bigcirc f)(3) = 36$ . $f(3) = 6$ , then $g(6) = 36$ .

Flashcard 59: Find $(g \bigcirc f)(x)$ if $f(x) = x^2$ and $g(x) = \frac{1}{x}$ .

Answer: $(g \bigcirc f)(x) = \frac{1}{x^2}$ . Apply $g$ to $f(x) = x^2$ : $\frac{1}{x^2}$ .

Flashcard 60: What is $(g \bigcirc f)(x)$ for $f(x) = \frac{1}{x}$ and $g(x) = x^2$ ?

Answer: $(g \bigcirc f)(x) = \frac{1}{x^2}$ . Apply $g$ to $f(x) = \frac{1}{x}$ : $(\frac{1}{x})^2$ .

Flashcard 61: If $f(x) = 2x + 1$ and $g(x) = x - 3$ , find $(f \bigcirc g)(x)$ .

Answer: $(f \bigcirc g)(x) = 2(x - 3) + 1$ . Substitute $g(x) = x - 3$ into $f$ .

Flashcard 62: If $f(x) = x - 4$ and $g(x) = x^2$ , find $(f \bigcirc g)(x)$ .

Answer: $(f \bigcirc g)(x) = x^2 - 4$ . Apply $f$ to $g(x) = x^2$ : $x^2 - 4$ .

Flashcard 63: State the notation for composing functions $f(x)$ and $g(x)$ .

Answer: $(f \bigcirc g)(x) = f(g(x))$ . Standard notation for function composition.

Flashcard 64: If $f(x) = x + 1$ and $g(x) = x^2$ , what is $(f \bigcirc g)(-2)$ ?

Answer: $(f \bigcirc g)(-2) = 5$ . $g(-2) = 4$ , then $f(4) = 5$ .

Flashcard 65: What is $(f \bigcirc g)(2)$ if $f(x) = 3x$ and $g(x) = x - 1$ ?

Answer: $(f \bigcirc g)(2) = 3$ . $g(2) = 1$ , then $f(1) = 3$ .

Flashcard 66: Find $(f \bigcirc g)(x)$ if $f(x) = x + 5$ and $g(x) = x^3$ .

Answer: $(f \bigcirc g)(x) = x^3 + 5$ . Apply $f$ to $g(x) = x^3$ : $x^3 + 5$ .

Flashcard 67: If $f(x) = x^2$ and $g(x) = 3x + 1$ , find $(g \bigcirc f)(x)$ .

Answer: $(g \bigcirc f)(x) = 3x^2 + 1$ . Apply $g$ to $f(x) = x^2$ : $g(x^2) = 3x^2 + 1$ .

Flashcard 68: Calculate $(f \bigcirc g)(x)$ if $f(x) = 2x + 1$ and $g(x) = x^3$ .

Answer: $(f \bigcirc g)(x) = 2x^3 + 1$ . Apply $f$ to $g(x) = x^3$ : $2x^3 + 1$ .

Flashcard 69: What is $(f \bigcirc g)(x)$ for $f(x) = \frac{1}{2}x$ and $g(x) = x + 4$ ?

Answer: $(f \bigcirc g)(x) = \frac{1}{2}(x + 4)$ . Apply $f$ to $g(x) = x + 4$ .

Flashcard 70: Determine $(g \bigcirc f)(x)$ if $f(x) = x + 1$ and $g(x) = x^3$ .

Answer: $(g \bigcirc f)(x) = (x + 1)^3$ . Apply $g$ to $f(x) = x + 1$ : $(x + 1)^3$ .

Flashcard 71: Calculate $(g \bigcirc f)(-3)$ for $f(x) = 3x + 1$ and $g(x) = x^2$ .

Answer: $(g \bigcirc f)(-3) = 64$ . $f(-3) = -8$ , then $g(-8) = 64$ .

Flashcard 72: Find $(f \bigcirc g)(x)$ if $f(x) = x + 5$ and $g(x) = x^3$ .

Answer: $(f \bigcirc g)(x) = x^3 + 5$ . Apply $f$ to $g(x) = x^3$ : $x^3 + 5$ .

AP Precalculus Flashcards: Composition Of Functions

Composition Of Functions

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Flashcard 1: Find (g◯f)(x)(g \bigcirc f)(x)(g◯f)(x) if f(x)=x+2f(x) = x + 2f(x)=x+2 and g(x)=3xg(x) = 3xg(x)=3x.

Flashcard 2: What is the definition of the composition of functions?

Flashcard 3: What is the definition of the composition of functions?

Flashcard 4: If f(x)=x−3f(x) = x - 3f(x)=x−3 and g(x)=x2g(x) = x^2g(x)=x2, find (f◯g)(x)(f \bigcirc g)(x)(f◯g)(x).

Flashcard 5: If f(x)=2xf(x) = 2xf(x)=2x and g(x)=x+3g(x) = x + 3g(x)=x+3, what is (f◯g)(x)(f \bigcirc g)(x)(f◯g)(x)?

Flashcard 6: Find (f◯g)(x)(f \bigcirc g)(x)(f◯g)(x) if f(x)=x2+1f(x) = x^2 + 1f(x)=x2+1 and g(x)=3xg(x) = 3xg(x)=3x.

Flashcard 7: Find (g◯f)(x)(g \bigcirc f)(x)(g◯f)(x) if f(x)=x2f(x) = x^2f(x)=x2 and g(x)=1xg(x) = \frac{1}{x}g(x)=x1​.

Flashcard 8: What is (g◯f)(5)(g \bigcirc f)(5)(g◯f)(5) for f(x)=3xf(x) = 3xf(x)=3x and g(x)=x−2g(x) = x - 2g(x)=x−2?

Flashcard 9: If f(x)=x2f(x) = x^2f(x)=x2 and g(x)=x+1g(x) = x + 1g(x)=x+1, what is (f◯g)(1)(f \bigcirc g)(1)(f◯g)(1)?

Flashcard 10: What is (f◯g)(0)(f \bigcirc g)(0)(f◯g)(0) for f(x)=2x+3f(x) = 2x + 3f(x)=2x+3 and g(x)=x2g(x) = x^2g(x)=x2?

Flashcard 11: If f(x)=x2f(x) = x^2f(x)=x2 and g(x)=3x+1g(x) = 3x + 1g(x)=3x+1, find (g◯f)(x)(g \bigcirc f)(x)(g◯f)(x).

Flashcard 12: What is (g◯f)(x)(g \bigcirc f)(x)(g◯f)(x) for f(x)=1xf(x) = \frac{1}{x}f(x)=x1​ and g(x)=x2g(x) = x^2g(x)=x2?

Flashcard 13: If f(x)=4xf(x) = 4xf(x)=4x and g(x)=x−2g(x) = x - 2g(x)=x−2, find (f◯g)(x)(f \bigcirc g)(x)(f◯g)(x).

Flashcard 14: What is (f◯g)(x)(f \bigcirc g)(x)(f◯g)(x) for f(x)=x3f(x) = x^3f(x)=x3 and g(x)=1xg(x) = \frac{1}{x}g(x)=x1​?

Flashcard 15: If f(x)=4xf(x) = 4xf(x)=4x and g(x)=x−2g(x) = x - 2g(x)=x−2, find (f◯g)(x)(f \bigcirc g)(x)(f◯g)(x).

Flashcard 16: If f(x)=1xf(x) = \frac{1}{x}f(x)=x1​ and g(x)=x+2g(x) = x + 2g(x)=x+2, find (f◯g)(x)(f \bigcirc g)(x)(f◯g)(x).

Flashcard 17: Determine (f◯g)(x)(f \bigcirc g)(x)(f◯g)(x) if f(x)=1/xf(x) = 1/xf(x)=1/x and g(x)=x−5g(x) = x - 5g(x)=x−5.

Flashcard 18: What is (f◯g)(2)(f \bigcirc g)(2)(f◯g)(2) if f(x)=3xf(x) = 3xf(x)=3x and g(x)=x−1g(x) = x - 1g(x)=x−1?

Flashcard 19: Write (f◯g)(x)(f \bigcirc g)(x)(f◯g)(x) for f(x)=x3f(x) = x^3f(x)=x3 and g(x)=1xg(x) = \frac{1}{x}g(x)=x1​.

Flashcard 20: Determine (g◯f)(x)(g \bigcirc f)(x)(g◯f)(x) if f(x)=x+1f(x) = x + 1f(x)=x+1 and g(x)=x3g(x) = x^3g(x)=x3.

Flashcard 21: If f(x)=x−3f(x) = x - 3f(x)=x−3 and g(x)=x2g(x) = x^2g(x)=x2, find (f◯g)(x)(f \bigcirc g)(x)(f◯g)(x).

Flashcard 22: Calculate (f◯g)(x)(f \bigcirc g)(x)(f◯g)(x) if f(x)=2x+1f(x) = 2x + 1f(x)=2x+1 and g(x)=x3g(x) = x^3g(x)=x3.

Flashcard 23: If f(x)=x2f(x) = x^2f(x)=x2 and g(x)=x+2g(x) = x + 2g(x)=x+2, find (g◯f)(x)(g \bigcirc f)(x)(g◯f)(x).

Flashcard 24: If f(x)=2x+1f(x) = 2x + 1f(x)=2x+1 and g(x)=x−3g(x) = x - 3g(x)=x−3, find (f◯g)(x)(f \bigcirc g)(x)(f◯g)(x).

Flashcard 25: Find (f◯g)(−1)(f \bigcirc g)(-1)(f◯g)(−1) if f(x)=x2f(x) = x^2f(x)=x2 and g(x)=x+5g(x) = x + 5g(x)=x+5.

Flashcard 26: If f(x)=x2f(x) = x^2f(x)=x2 and g(x)=x+1g(x) = x + 1g(x)=x+1, what is (f◯g)(1)(f \bigcirc g)(1)(f◯g)(1)?

Flashcard 27: Find (g◯f)(0)(g \bigcirc f)(0)(g◯f)(0) for f(x)=x2+1f(x) = x^2 + 1f(x)=x2+1 and g(x)=2xg(x) = 2xg(x)=2x.

Flashcard 28: Determine (f◯g)(x)(f \bigcirc g)(x)(f◯g)(x) for f(x)=x2f(x) = x^2f(x)=x2 and g(x)=x+1g(x) = x + 1g(x)=x+1.

Flashcard 29: If f(x)=5xf(x) = 5xf(x)=5x and g(x)=x−3g(x) = x - 3g(x)=x−3, find (f◯g)(x)(f \bigcirc g)(x)(f◯g)(x).

Flashcard 30: Determine (f◯g)(1)(f \bigcirc g)(1)(f◯g)(1) if f(x)=x−2f(x) = x - 2f(x)=x−2 and g(x)=x2g(x) = x^2g(x)=x2.

Flashcard 31: What is (f◯g)(x)(f \bigcirc g)(x)(f◯g)(x) for f(x)=x3f(x) = x^3f(x)=x3 and g(x)=1xg(x) = \frac{1}{x}g(x)=x1​?

Flashcard 32: If f(x)=5xf(x) = 5xf(x)=5x and g(x)=x−3g(x) = x - 3g(x)=x−3, find (f◯g)(x)(f \bigcirc g)(x)(f◯g)(x).

Flashcard 33: If f(x)=1xf(x) = \frac{1}{x}f(x)=x1​ and g(x)=x+2g(x) = x + 2g(x)=x+2, find (f◯g)(x)(f \bigcirc g)(x)(f◯g)(x).

Flashcard 34: Write (f◯g)(x)(f \bigcirc g)(x)(f◯g)(x) for f(x)=x3f(x) = x^3f(x)=x3 and g(x)=1xg(x) = \frac{1}{x}g(x)=x1​.

Flashcard 35: What is (g◯f)(5)(g \bigcirc f)(5)(g◯f)(5) for f(x)=3xf(x) = 3xf(x)=3x and g(x)=x−2g(x) = x - 2g(x)=x−2?

Flashcard 36: If f(x)=x2f(x) = x^2f(x)=x2 and g(x)=x+2g(x) = x + 2g(x)=x+2, find (g◯f)(x)(g \bigcirc f)(x)(g◯f)(x).

Flashcard 37: If f(x)=2x+3f(x) = 2x + 3f(x)=2x+3, find (f◯f)(x)(f \bigcirc f)(x)(f◯f)(x).

Flashcard 38: If f(x)=x2+2f(x) = x^2 + 2f(x)=x2+2 and g(x)=4xg(x) = 4xg(x)=4x, find (f◯g)(x)(f \bigcirc g)(x)(f◯g)(x).

Flashcard 39: Find (g◯f)(x)(g \bigcirc f)(x)(g◯f)(x) if f(x)=x+2f(x) = x + 2f(x)=x+2 and g(x)=3xg(x) = 3xg(x)=3x.

Flashcard 40: Find (f◯g)(x)(f \bigcirc g)(x)(f◯g)(x) if f(x)=x2+1f(x) = x^2 + 1f(x)=x2+1 and g(x)=3xg(x) = 3xg(x)=3x.

Flashcard 41: Find (f◯g)(−1)(f \bigcirc g)(-1)(f◯g)(−1) if f(x)=x2f(x) = x^2f(x)=x2 and g(x)=x+5g(x) = x + 5g(x)=x+5.

Flashcard 42: If f(x)=x2+2f(x) = x^2 + 2f(x)=x2+2 and g(x)=4xg(x) = 4xg(x)=4x, find (f◯g)(x)(f \bigcirc g)(x)(f◯g)(x).

Flashcard 43: What is (f◯g)(0)(f \bigcirc g)(0)(f◯g)(0) for f(x)=2x+3f(x) = 2x + 3f(x)=2x+3 and g(x)=x2g(x) = x^2g(x)=x2?

Flashcard 44: Calculate (g◯f)(3)(g \bigcirc f)(3)(g◯f)(3) for f(x)=2xf(x) = 2xf(x)=2x and g(x)=x2g(x) = x^2g(x)=x2.

Flashcard 45: What is (f◯g)(x)(f \bigcirc g)(x)(f◯g)(x) for f(x)=12xf(x) = \frac{1}{2}xf(x)=21​x and g(x)=x+4g(x) = x + 4g(x)=x+4?

Flashcard 46: Calculate (g◯f)(−3)(g \bigcirc f)(-3)(g◯f)(−3) for f(x)=3x+1f(x) = 3x + 1f(x)=3x+1 and g(x)=x2g(x) = x^2g(x)=x2.

Flashcard 47: Find (g◯f)(0)(g \bigcirc f)(0)(g◯f)(0) for f(x)=x2+1f(x) = x^2 + 1f(x)=x2+1 and g(x)=2xg(x) = 2xg(x)=2x.

Flashcard 48: Determine (f◯g)(x)(f \bigcirc g)(x)(f◯g)(x) if f(x)=1/xf(x) = 1/xf(x)=1/x and g(x)=x−5g(x) = x - 5g(x)=x−5.

Flashcard 49: Evaluate (g◯f)(2)(g \bigcirc f)(2)(g◯f)(2) if f(x)=x+1f(x) = x + 1f(x)=x+1 and g(x)=2xg(x) = 2xg(x)=2x.

Flashcard 50: State the notation for composing functions f(x)f(x)f(x) and g(x)g(x)g(x).

Flashcard 51: If f(x)=2x+3f(x) = 2x + 3f(x)=2x+3, find (f◯f)(x)(f \bigcirc f)(x)(f◯f)(x).

Flashcard 52: If f(x)=x−4f(x) = x - 4f(x)=x−4 and g(x)=x2g(x) = x^2g(x)=x2, find (f◯g)(x)(f \bigcirc g)(x)(f◯g)(x).

Flashcard 53: If f(x)=x+1f(x) = x + 1f(x)=x+1 and g(x)=x2g(x) = x^2g(x)=x2, what is (f◯g)(−2)(f \bigcirc g)(-2)(f◯g)(−2)?

Flashcard 54: Determine (f◯g)(x)(f \bigcirc g)(x)(f◯g)(x) for f(x)=x2f(x) = x^2f(x)=x2 and g(x)=x+1g(x) = x + 1g(x)=x+1.

Flashcard 55: Determine (f◯g)(1)(f \bigcirc g)(1)(f◯g)(1) if f(x)=x−2f(x) = x - 2f(x)=x−2 and g(x)=x2g(x) = x^2g(x)=x2.

Flashcard 56: Evaluate (g◯f)(2)(g \bigcirc f)(2)(g◯f)(2) if f(x)=x+1f(x) = x + 1f(x)=x+1 and g(x)=2xg(x) = 2xg(x)=2x.

Flashcard 57: If f(x)=2xf(x) = 2xf(x)=2x and g(x)=x+3g(x) = x + 3g(x)=x+3, what is (f◯g)(x)(f \bigcirc g)(x)(f◯g)(x)?

Flashcard 58: Calculate (g◯f)(3)(g \bigcirc f)(3)(g◯f)(3) for f(x)=2xf(x) = 2xf(x)=2x and g(x)=x2g(x) = x^2g(x)=x2.

Flashcard 59: Find (g◯f)(x)(g \bigcirc f)(x)(g◯f)(x) if f(x)=x2f(x) = x^2f(x)=x2 and g(x)=1xg(x) = \frac{1}{x}g(x)=x1​.

Flashcard 60: What is (g◯f)(x)(g \bigcirc f)(x)(g◯f)(x) for f(x)=1xf(x) = \frac{1}{x}f(x)=x1​ and g(x)=x2g(x) = x^2g(x)=x2?

Flashcard 61: If f(x)=2x+1f(x) = 2x + 1f(x)=2x+1 and g(x)=x−3g(x) = x - 3g(x)=x−3, find (f◯g)(x)(f \bigcirc g)(x)(f◯g)(x).

Flashcard 62: If f(x)=x−4f(x) = x - 4f(x)=x−4 and g(x)=x2g(x) = x^2g(x)=x2, find (f◯g)(x)(f \bigcirc g)(x)(f◯g)(x).

Flashcard 63: State the notation for composing functions f(x)f(x)f(x) and g(x)g(x)g(x).

Flashcard 64: If f(x)=x+1f(x) = x + 1f(x)=x+1 and g(x)=x2g(x) = x^2g(x)=x2, what is (f◯g)(−2)(f \bigcirc g)(-2)(f◯g)(−2)?

Flashcard 65: What is (f◯g)(2)(f \bigcirc g)(2)(f◯g)(2) if f(x)=3xf(x) = 3xf(x)=3x and g(x)=x−1g(x) = x - 1g(x)=x−1?

Flashcard 66: Find (f◯g)(x)(f \bigcirc g)(x)(f◯g)(x) if f(x)=x+5f(x) = x + 5f(x)=x+5 and g(x)=x3g(x) = x^3g(x)=x3.

Flashcard 67: If f(x)=x2f(x) = x^2f(x)=x2 and g(x)=3x+1g(x) = 3x + 1g(x)=3x+1, find (g◯f)(x)(g \bigcirc f)(x)(g◯f)(x).

Flashcard 68: Calculate (f◯g)(x)(f \bigcirc g)(x)(f◯g)(x) if f(x)=2x+1f(x) = 2x + 1f(x)=2x+1 and g(x)=x3g(x) = x^3g(x)=x3.

Flashcard 69: What is (f◯g)(x)(f \bigcirc g)(x)(f◯g)(x) for f(x)=12xf(x) = \frac{1}{2}xf(x)=21​x and g(x)=x+4g(x) = x + 4g(x)=x+4?

Flashcard 70: Determine (g◯f)(x)(g \bigcirc f)(x)(g◯f)(x) if f(x)=x+1f(x) = x + 1f(x)=x+1 and g(x)=x3g(x) = x^3g(x)=x3.

Flashcard 71: Calculate (g◯f)(−3)(g \bigcirc f)(-3)(g◯f)(−3) for f(x)=3x+1f(x) = 3x + 1f(x)=3x+1 and g(x)=x2g(x) = x^2g(x)=x2.

Flashcard 72: Find (f◯g)(x)(f \bigcirc g)(x)(f◯g)(x) if f(x)=x+5f(x) = x + 5f(x)=x+5 and g(x)=x3g(x) = x^3g(x)=x3.