Algebra and Functions Flashcards

If f(x) = 3x - 2 and g(x) = x + 4, what is f(g(2))?

Answer: 16

g(2) = 2+4 = 6. f(6) = 3(6)-2 = 16.

A function f is defined by f(x) = 2x + 1 for x < 0 and f(x) = x² - 1 for x ≥ 0. What is f(-3) + f(2)?

Answer: 2

f(-3) = 2(-3)+1 = -5. f(2) = 4-1 = 3. Sum = -5+3 = -2. Wait: -5+3=-2, not 2. Let me recheck: f(-3)=2(-3)+1=-6+1=-5; f(2)=2²-1=3; total=-2. Correcting answer to -2.

If f(x) = x² - 4 and f(a) = 12, what are the possible values of a?

Answer: a = 4 or a = -4

a²-4 = 12 → a² = 16 → a = ±4.

The function h(x) = -2|x - 3| + 6. What is the maximum value of h(x)?

Answer: 6

Since -2|x-3| ≤ 0, the maximum occurs when |x-3| = 0, i.e., x=3. h(3) = 0+6 = 6.

If f(x) = 5x + 2 and f⁻¹ is the inverse function, what is f⁻¹(17)?

Answer: 3

If f(x)=17: 5x+2=17, 5x=15, x=3. So f⁻¹(17)=3.

Which of the following represents an odd function?

Answer: f(x) = x³ - x

A function is odd if f(-x) = -f(x). For x³-x: f(-x) = -x³+x = -(x³-x) = -f(x) ✓.

The domain of f(x) = √(2x - 6) is x ≥ k. What is the value of k?

Answer: 3

For the square root to be real: 2x-6 ≥ 0, so 2x ≥ 6, x ≥ 3. Thus k = 3.

If g(t) = t/(t-2) for t ≠ 2, what is g(g(6))?

Answer: 3/2

g(6) = 6/(6-2) = 6/4 = 3/2. g(3/2) = (3/2)/(3/2-2) = (3/2)/(-1/2) = -3.