algebra questions

Question

1. Explain step by step how to determine if two functions are inverses of each other. Provide a detailed example.

Answer 1

Two functions f(x) and g(x) are inverses if:

f(g(x)) = g(f(x))

example:

f(x) = 2x - 3

g(x) = (x + 3)/2

f(g(x)) = 2[(x+3)/2] - 3 = x

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