Chapter 4, Exponential and Logarithmic Functions - Section 4.3 - Logarithmic Functions - 4.3 Exercises - Page 389: 87

The domain of $(f \circ g) (x)$ is $(2,\infty)$ The domain of $(g \circ f)(x)$ is $(0,\infty)$

We are given: $f(x)=\log_{2}x$ $g(x)=x-2$ $(f \circ g) (x)=f(g(x))=\log_{2}{(x-2)}$ $(g \circ f)(x)=g(f(x))=\log_{2}x-2$ The domain of $(f \circ g) (x)$ is $(2,\infty)$ and $(g \circ f)(x)$ is $(0,\infty)$