Bluebook SAT Test Bluebook SAT Math: Advanced Functions Questions and Answers 4

Question 1

Let f(x) = x/(x + 2) and g(x) = (x + 2)/(x − 1). For which values of x is f(g(x)) undefined?

Accepted Answer

x = 0 and x = 1

Answer

f(g(x)) is undefined when (1) g(x) itself is undefined, or (2) g(x) lands on a value that makes f undefined. g(x) is undefined at x = 1. f is undefined when its input equals −2, so set g(x) = −2: (x+2)/(x−1) = −2 → x+2 = −2x+2 → 3x = 0 → x = 0. Thus f(g(x)) is undefined at x = 0 and x = 1.

Question 2

A function h is defined as h(x) = 2f(3x − 6) + 5, where f is some function. The graph of f has a local maximum at the point (4, 7). What are the coordinates of the corresponding local maximum on the graph of h?

Accepted Answer

(10/3, 19)

Answer

To find the x-coordinate on h corresponding to x = 4 on f, solve 3x − 6 = 4, giving x = 10/3. The y-coordinate becomes h(10/3) = 2f(4) + 5 = 2(7) + 5 = 19. So the local maximum on h is at (10/3, 19).

Question 3

If f(x) = √(4x − 3) + 1, what is f⁻¹(5)?

Accepted Answer

19/4

Answer

Set f(x) = 5: √(4x − 3) + 1 = 5 → √(4x − 3) = 4 → 4x − 3 = 16 → 4x = 19 → x = 19/4. So f⁻¹(5) = 19/4.

Question 4

Let p(x) be a polynomial such that p(x + 2) = x³ − 3x + 4 for all real x. What is p(0)?

Accepted Answer

2

Answer

To find p(0), we need the input of p to equal 0, so set x + 2 = 0, giving x = −2. Then p(0) = p(−2 + 2) = (−2)³ − 3(−2) + 4 = −8 + 6 + 4 = 2.

Question 5

A function g satisfies g(g(x)) = x for all real numbers x. If g(3) = 7, what is the value of g(7) + g(3)?

Accepted Answer

10

Answer

Since g(g(x)) = x, g is its own inverse. Applying this with x = 3: g(g(3)) = 3, so g(7) = 3. Therefore g(7) + g(3) = 3 + 7 = 10.

Bluebook SAT Practice Test

Bluebook SAT Practice Test

Bluebook SAT Test Bluebook SAT Math: Advanced Functions Questions and Answers 4