Free ACT Math: Functions Questions and Answers 2 Flashcards

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

Answer: g⁻¹(x) = (x + 5)/3

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.

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

Answer: x ≥ 4

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

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

Answer: (x + 3)²

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

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

Answer: 1

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.

Which of the following represents a function?

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

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.

If f(x) = 4x − 1 and f(a) = 11, what is the value of a?

Answer: 3

f(a) = 4a − 1 = 11. Add 1: 4a = 12. Divide by 4: a = 3.