Question

Determine if f(x) and g(x) are inverse functions using composition of functions.

f(x) = -4x - 20
g(x) = -1x - 5
A) Yes, they are inverse functions.
B) No, they are not inverse functions.
C) It cannot be determined.
D) More information is needed.

Answer 1

To determine if two functions are inverse functions, we need to check the composition of the functions. In this case, both compositions result in x, indicating that f(x) and g(x) are inverse functions.

Step-by-step explanation:

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

Given f(x) = -4x - 20 and g(x) = -1x - 5, we can substitute g(x) into f(x) and vice versa to check if the composition is the identity function.

f(g(x)) = -4(-1x - 5) - 20 = 4x + 20 - 20 = 4x = x

g(f(x)) = -1(-4x - 20) - 5 = 4x + 20 - 5 = 4x + 15 = x

Since both compositions result in x, the functions f(x) and g(x) are inverse functions. Therefore, the correct answer is A) Yes, they are inverse functions.