Free ACT Math: Functions Questions and Answers 2 — Questions and Answers
Question 1: If g(x) = 3x − 5, what is g⁻¹(x) (the inverse function)?
- g⁻¹(x) = (x + 5)/3 (Correct answer)
- g⁻¹(x) = 3x + 5
- g⁻¹(x) = (x − 5)/3
- g⁻¹(x) = x/3 − 5
Correct 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.
Question 2: For the function h(x) = √(x − 4), what is the domain?
- x ≥ 4 (Correct answer)
- x > 4
- x ≥ 0
- All real numbers
Correct 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, ∞).
Question 3: If f(x) = x² and g(x) = x + 3, what is (f ∘ g)(x)?
- (x + 3)² (Correct answer)
- x² + 3
- x³ + 3x²
- (x² + 3)²
Correct 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.
Question 4: A function f is defined as f(x) = |x − 2| + 1. What is the minimum value of f(x)?
- 1 (Correct answer)
- 0
- 2
- 3
Correct 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.
Question 5: Which of the following represents a function?
- {(1,2), (3,4), (5,6), (7,8)} (Correct answer)
- {(1,2), (1,3), (2,4), (3,5)}
- {(2,3), (4,3), (2,5), (6,7)}
- {(1,1), (2,2), (2,3), (3,4)}
Correct 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.
Question 6: If f(x) = 4x − 1 and f(a) = 11, what is the value of a?
- 3 (Correct answer)
- 2.5
- 4
- 48
Correct answer: 3
f(a) = 4a − 1 = 11. Add 1: 4a = 12. Divide by 4: a = 3.
Free ACT Math: Functions Questions and Answers 2
If g(x) = 3x − 5, what is g⁻¹(x) (the inverse function)?