Consider the following functions: f(x) = x/x+7, g(x) = 2x-7. Find (g o g)(x) and the domain of (g o g)(x).

Question

Consider the following functions: f(x) = x/x+7, g(x) = 2x-7.

Find (g o g)(x) and the domain of (g o g)(x) using interval notation.

Thank you for your help.

Answer 1

( g o g)(x) = g(g(x)) = g(2x-7) = (2(2x-7)-7) = 4x-14-7 = 4x-21

( g o g)(x) =4x-21

domain of (g o g)(x) = (infty , -infty )

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.