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All Common Core: High School - Functions Resources

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Flashcards: Invertible and Non-Invertible Functions: CCSS.Math.Content.HSF-BF.B.4d

What is the inverse of the following function?

$f(x)=\frac{1}{4}x^2$

Screen shot 2016 01 19 at 12.30.45 pm

Screen shot 2016 01 19 at 12.31.06 pm

Screen shot 2016 01 19 at 12.36.01 pm

Screen shot 2016 01 19 at 12.34.36 pm

Screen shot 2016 01 19 at 12.34.19 pm

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Flashcards: Invertible and Non-Invertible Functions: CCSS.Math.Content.HSF-BF.B.4d

What is the inverse of the following function?

$f(x)=\frac{1}{4}x^2$

Your answer:

Screen shot 2016 01 19 at 12.30.45 pm

Your answer:

Screen shot 2016 01 19 at 12.36.01 pm

Your answer:

Screen shot 2016 01 19 at 12.34.36 pm

Your answer:

Screen shot 2016 01 19 at 12.34.19 pm

Correct answer:

Screen shot 2016 01 19 at 12.31.06 pm

Explanation:

This question is testing ones ability to understand what it means for a function to be invertible or non-invertible and how to find the inverse of a non-invertible function through means of domain restriction.

For the purpose of Common Core Standards, "Produce an invertible function from a non-invertible function by restricting the domain." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.4d). It is important to note that this standard is not directly tested on but, it is used for building a deeper understanding on invertible and non-invertible functions and their inverses.

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Determine whether the function given is invertible or non-invertible.

Using technology to graph the function f(x) results in the following graph.

Screen shot 2016 01 19 at 12.16.35 pm

This function is non-invertible because when taking the inverse, the graph will become a parabola opening to the right which is not a function. A sideways opening parabola contains two outputs for every input which by definition, is not a function.

Step 2: Make the function invertible by restricting the domain.

To make the given function an invertible function, restrict the domain to $x\geq0$ which results in the following graph.

Screen shot 2016 01 19 at 12.30.45 pm

Step 3: Graph the inverse of the invertible function.

Swapping the coordinate pairs of the given graph results in the inverse.

Screen shot 2016 01 19 at 12.16.28 pm

The inverse graphed alone is as follows.

Flashcards: Invertible and Non-Invertible Functions: CCSS.Math.Content.HSF-BF.B.4d

What is the inverse of the following function?

f(x)=2x^2

$f^{-1}(x)=\sqrt{\frac{x}{4}}$

$f^{-1}(x)=\sqrt{\frac{x}{2}}$

$f^{-1}(x)=4\sqrt{x}$

$f^{-1}(x)=2\sqrt{x}$

$f^{-1}(x)=\sqrt{x}$

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Flashcards: Invertible and Non-Invertible Functions: CCSS.Math.Content.HSF-BF.B.4d

What is the inverse of the following function?

f(x)=2x^2

Your answer:

$f^{-1}(x)=\sqrt{\frac{x}{4}}$

Your answer:

$f^{-1}(x)=4\sqrt{x}$

Your answer:

$f^{-1}(x)=2\sqrt{x}$

Your answer:

$f^{-1}(x)=\sqrt{x}$

Correct answer:

$f^{-1}(x)=\sqrt{\frac{x}{2}}$

Explanation:

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Determine whether the function given is invertible or non-invertible.

Using technology to graph the function f(x) results in the following graph.

Step 2: Make the function invertible by restricting the domain.

To make the given function an invertible function, restrict the domain to $x\geq0$ which results in the following graph.

Q2 2

Step 3: Graph the inverse of the invertible function.

Swapping the coordinate pairs of the given graph results in the inverse.

Q2 3

Therefore, the inverse of this function algebraically

$f^{-1}(x)=\sqrt{\frac{x}{2}}$ .

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All Common Core: High School - Functions Resources

Flashcards: Invertible and Non-Invertible Functions: CCSS.Math.Content.HSF-BF.B.4d

Flashcards: Invertible and Non-Invertible Functions: CCSS.Math.Content.HSF-BF.B.4d

Flashcards: Invertible and Non-Invertible Functions: CCSS.Math.Content.HSF-BF.B.4d

Flashcards: Invertible and Non-Invertible Functions: CCSS.Math.Content.HSF-BF.B.4d

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