College Math Placement Test Functions 3

Question 1

What is the inverse of f(x) = (x + 3) / 2?

Accepted Answer

f⁻¹(x) = 2x - 3

Answer

Swap x and y: x = (y+3)/2 → 2x = y+3 → y = 2x - 3.

Question 2

The function f(x) = -|x - 2| + 5 has a maximum value of:

Accepted Answer

5

Answer

The absolute value is always ≥ 0, so -|x-2| ≤ 0, and f(x) ≤ 5; the maximum is 5 at x = 2.

Question 3

If f(x) = x² and g(x) = x + 1, which expression equals (g ∘ f)(x)?

Accepted Answer

x² + 1

Answer

g(f(x)) = g(x²) = x² + 1.

Question 4

Which value of x is NOT in the domain of f(x) = 1 / (x² - 9)?

Accepted Answer

x = 3

Answer

x² - 9 = 0 when x = ±3, making the denominator zero, so x = 3 is excluded.

Question 5

If f(x) = 4x - 1, what is f(f(2))?

Accepted Answer

28

Answer

f(2) = 4(2) - 1 = 7; f(7) = 4(7) - 1 = 27.

College Math Placement Test Practice Test