College Math Placement Test Functions 3 — Questions and Answers
Question 1: What is the inverse of f(x) = (x + 3) / 2?
- f⁻¹(x) = 2x - 3 (Correct answer)
- f⁻¹(x) = 2x + 3
- f⁻¹(x) = (x - 3) / 2
- f⁻¹(x) = x/2 + 3
Correct answer: f⁻¹(x) = 2x - 3
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:
- 2
- 5 (Correct answer)
- 7
- -5
Correct answer: 5
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)?
- x² + 2x + 1
- x² + 1 (Correct answer)
- (x+1)²
- x³ + x²
Correct answer: x² + 1
g(f(x)) = g(x²) = x² + 1.
Question 4: Which value of x is NOT in the domain of f(x) = 1 / (x² - 9)?
- x = 0
- x = 1
- x = 3 (Correct answer)
- x = -1
Correct answer: x = 3
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))?
- 7
- 27
- 28 (Correct answer)
- 31
Correct answer: 28
f(2) = 4(2) - 1 = 7; f(7) = 4(7) - 1 = 27.
Question 6: A function f has the property that f(-x) = f(x) for all x. This means f is:
- Odd
- Even (Correct answer)
- One-to-one
- Onto
Correct answer: Even
A function satisfying f(-x) = f(x) is called an even function and is symmetric about the y-axis.
Question 7: Which of the following is the range of f(x) = 3 / (x² + 1)?
- All real numbers
- (0, 3] (Correct answer)
- [0, 3)
- (-∞, 3]
Correct answer: (0, 3]
Since x² + 1 ≥ 1, we have 0 < 3/(x²+1) ≤ 3, so the range is (0, 3].
College Math Placement Test Functions 3
What is the inverse of f(x) = (x + 3) / 2?