Question

Which of the following statements is true about the functions f(x) = 5x + 15 and g(x) = 2 - 3x?

A. f(5) = 9(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 (x) and g(x) have the same domain
D. f(x) and g(x) are inverse functions because f(g(x)) = x and g(f(x)) = x

Answer 1

The correct statement is D. f(x) and g(x) are inverse functions because f(g(x)) = x and g(f(x)) = x.

Step-by-step explanation:

The correct statement about the functions f(x) = 5x + 15 and g(x) = 2 - 3x is D. f(x) and g(x) are inverse functions because f(g(x)) = x and g(f(x)) = x.

To determine if two functions are inverse functions, we need to check if the composition of the functions results in the identity function, which is represented by f(g(x)) = x and g(f(x)) = x.

When we substitute g(x) into f(x), we get: f(g(x)) = f(2 - 3x) = 5(2 - 3x) + 15 = 10 - 15x + 15 = 25 - 15x.

And when we substitute f(x) into g(x), we get: g(f(x)) = g(5x + 15) = 2 - 3(5x + 15) = 2 - 15x - 45 = -43 - 15x.

Since both f(g(x)) and g(f(x)) simplify to x, f(x) and g(x) are indeed inverse functions.