Question

Use composition of functions to determine whether f and g are inverse functions:

f(x)=(x/3)-2 and g(x)=3x+6

Answer 1

By composing functions f and g, we find out that both f(g(x)) and g(f(x)) equal x, which proves that f and g are inverse functions.

Step-by-step explanation:

To determine whether the functions f and g are inverse functions, we can compose them and see if the result is the identity function, which is f(g(x)) = x and g(f(x)) = x.

First, we find f(g(x)):
f(g(x)) = f(3x + 6)
= ((3x + 6)/3) - 2
= x + 2 - 2
= x

Second, we find g(f(x)):
g(f(x)) = g((x/3) - 2)
= 3((x/3) - 2) + 6
= x - 6 + 6
= x

Since f(g(x)) = x and g(f(x)) = x, the functions f and g are indeed inverse functions of each other.