Question

Which of the following statements is true about the functions f(x)=5x+15 and g(x)=1/5x-3?

A. f(5) = g(5) because f(x) and g(x) are inverse functions.
B. f(-5) = g(5) because f(x) and g(x) are inverse functions.
C. f(x) and g(x) are inverse functions because f(x) and g(x) have the same domain.
D. f(x) and g(x) are inverse functions because f∘g = x and g∘f = x.

Answer 1

The true statement is D. f(x) and g(x) are inverse functions because composing one with the other yields the identity function, x.

Step-by-step explanation:

The statement that is true about the functions f(x)=5x+15 and g(x)=1/5x-3 is D. f(x) and g(x) are inverse functions because f∘g = x and g∘f = x. This is verified by composing the functions: f(g(x)) and g(f(x)).

Let's do the composition:

1. Compute f(g(x)): f(g(x)) = f(1/5x - 3) = 5(1/5x - 3) + 15 = x - 3*5 + 15 = x
2. Compute g(f(x)): g(f(x)) = g(5x + 15) = 1/5(5x + 15) - 3 = x + 3 - 3 = x

Both compositions result in the identity function x, confirming that f(x) and g(x) are indeed inverse functions.