Free ACT Math: Functions Questions and Answers 2

Question 1

If g(x) = 3x − 5, what is g⁻¹(x) (the inverse function)?

Accepted Answer

g⁻¹(x) = (x + 5)/3

Answer

To find inverse: swap x and y, then solve for y. y = 3x − 5 → x = 3y − 5 → x + 5 = 3y → y = (x + 5)/3. So g⁻¹(x) = (x + 5)/3.

Question 2

For the function h(x) = √(x − 4), what is the domain?

Accepted Answer

x ≥ 4

Answer

The square root requires the expression under the radical to be non-negative: x − 4 ≥ 0 → x ≥ 4. The domain is [4, ∞).

Question 3

If f(x) = x² and g(x) = x + 3, what is (f ∘ g)(x)?

Accepted Answer

(x + 3)²

Answer

Composition (f ∘ g)(x) = f(g(x)) = f(x + 3) = (x + 3)². The output of g is the input of f.

Question 4

A function f is defined as f(x) = |x − 2| + 1. What is the minimum value of f(x)?

Accepted Answer

1

Answer

The expression |x − 2| ≥ 0 for all x, with minimum 0 when x = 2. So f(2) = 0 + 1 = 1. The minimum value is 1.

Question 5

Which of the following represents a function?

Accepted Answer

{(1,2), (3,4), (5,6), (7,8)}

Answer

A function requires each input (x-value) to map to exactly one output. In option A, each x-value (1,3,5,7) appears only once. Options B, C, and D each have x-values that repeat with different outputs.

ACT Practice Test

ACT Practice Test

Free ACT Math: Functions Questions and Answers 2