Question

Which pairs of function are inverses of each other?

Choose all answers that are correct.

f(x) = 5x + 10 and g(x) = 0.2x -2

f(x) = x^2 + 3 and g(x) = ± √x+3

f(x) = 1/2x + 7 and g(x) = 2x -7

f(x) = 1/4x -1 and g(x) = 4x + 4

Answer 1

• f(x) = 5x + 10 and g(x) = 0.2x -2
• f(x) = 1/4x -1 and g(x) = 4x + 4

Explanation:

f and g will be inverses if f(g(x)) = x.

A — f(g(x)) = 5(0.2x -2) +10 = x -10 +10 = x . . . . . inverses

B — f(g(x)) = (±√x+3)^2 +3 = x ±6√x +9 +3 ≠ x . . . . . not inverses

(even if it is g(x) = ±√(x+3), the functions are still not inverses)

C — 1/2(2x -7) +7 = x -7/2 +7 = x +7/2 ≠ x . . . . . not inverses

D — 1/4(4x +4) -1 = x +1 -1 = x . . . . . inverses