How to find f(x) - SAT Math

Explanation: The values of each answer are A)3 B) 2, C) 1, D)4, E)5.

Subtract the first expression from the second. That gives you 6z = 6. That simplifies to z = 1.

When functions are set up within other functions like in this problem, the function closest to the given variable is performed first. The value obtained from this function is then plugged in as the variable in the outside function. Since b(x) = –2x, and x = 2, the value we obtain from b(x) is –4. We then plug this value in for x in the a(x) function. So a(x) then becomes 2(–43) + (–4), which equals –132.

For this question, we "plug in" the value of x given, which is inside the parentheses, and follow along the table to see what value the f or g functions output. For g(12), the output value is –1, while for f(9), the output value is 4 (be careful not to reverse these!) Thus, we can plug into the equation given:

(–1) – √4) = –1 – 2 = –3.

g is a function of f, and f is a function of 3, so you must work inside out.

f(3) = 11

g(f(3)) = g(11) = 121 + 11 = 132

f(x, y) is defined as x2y2 – xy + y. In order to find f(a, b), we will need to first find a and then b.

We are told that a = f(1, 3). We can use the definition of f(x, y) to determine the value of a.

a = f(1, 3) = 1232 – 1(3) + 3 = 1(9) – 3 + 3 = 9 + 0 = 9

a = 9

Similarly, we can find b by determining the value of f(–2, –1).

b = f(–2, –1) = (–2)2(–1)2 – (–2)(–1) + –1 = 4(1) – (2) – 1 = 4 – 2 – 1 = 1

b = 1

Now, we can find f(a, b), which is equal to f(9, 1).

f(a, b) = f(9, 1) = 92(12) – 9(1) + 1 = 81 – 9 + 1 = 73

f(a, b) = 73

The answer is 73.

Using the defined function, f(a) will produce the same result when substituted for x:

f(a) = _a_2 – 5

Setting this equal to 4, you can solve for a:

_a_2 – 5 = 4

_a_2 = 9

a = –3 or 3

The function g(x) is equal to 4_x_ + 5, and the notation 2_g_(x) asks us to multiply the entire function by 2. 2(4_x_ + 5) = 8_x_ + 10. We then subtract 3, the second part of the new equation, to get 8_x_ + 7.

First you must find what g(4) is. The definition of g(x) tells you that the function is always equal to 2, regardless of what “x” is. Plugging 2 into f(x), we get 22 + 5(2) = 14.

Substitute 3 for all a.

(1/3) * (33 + 5(3) – 15)

(1/3) * (27 + 15 – 15)

(1/3) * (27) = 9

Begin by solving g(6) first.

g(6) = –(1/2)(6) – 5

g(6) = –3 – 5

g(6) = –8

We substitute f(–8)

f(–8) = (–8)2 – 6

f(–8) = 64 – 6

f(–8) = 58

If x = –10, then (_x_2 – 175) = 100 – 175 = –75. But the sign |x| means the absolute value of x. Absolute values are always positive.

|–75| = 75

By plugging in –2 for x and evaluating, the answer becomes 8 – 10 – 3 = -5.

To find f(g(x) plug the equation for g(x) into equation f(x) in place of “x” so that you have: f(g(x)) = (3x + 5)² – 2.

Simplify: (3x + 5)(3x + 5) – 2

Use FOIL: 9x² + 30x + 25 – 2 = 9x² + 30x + 23

With composition of functions (as with the order of operations) we perform what is inside of the parentheses first. So, g(3)=2(3)+2=8 and then f(8)=24.

Substitute -1 for in the given function.

If you didn’t remember the negative sign, you will have calculated 36. If you remembered the negative sign at the very last step, you will have calculated -36; however, if you did not remember that is 1, then you will have calculated 18.

To evaluate f(g(4)), one must first determine the value of g(4), then plug that into f(x).

g(4) = 2 x 4 – 7 = 1.

f(1) = 2 x 12 + 2 x 1 – 3 = 0.

There are two ways to do this problem. The first way just involves plugging in –3 for x and solving 6〖(–3)〗2 + 16(–3) – 6, which equals 54 – 48 – 6 = 0. The second way involves factoring the polynomial to (6x – 2)(x + 3) and then plugging in –3 for x. The second way quickly shows that the answer is 0 due to multiplying by (–3 + 3).

We can think of k❋ as the function f(k)=(k-1)(k+2), so 3❋+4❋is f(3)+f(4). When we plug 3 into the function, we find f(3)=(3-1)(3+2)=(2)(5)=10, and when we plug 4 into the function, we find f(4)=(4-1)(4+2)=(3)(6)=18, so f(3)+f(4)=10+18=28. The only answer choice that equals 28 is 5❋ which is f(5)=(5-1)(5+2)=(4)(7)=28.

First we substitute in 12 for x and set the equation up as 12-t=4. We then get t=8, and substitute that for t and get f(0.5*8), giving us f(4). Plugging 4 in for x, and using t=8 that we found before, gives us:

f(4) = 4 - 8 = -4