Chapter 4, Exponential and Logarithmic Functions - Section 4.3 - Logarithmic Functions - 4.3 Exercises - Page 389: 86

The domain of both $(f \circ g) (x)$ and $(g \circ f)(x)$ is $(-\infty,\infty)$

We are given: $f(x)=3^x$ $g(x)=x^2+1$ $(f \circ g) (x)=f(g(x))=3^{x^2+1}$ $(g \circ f)(x)=g(f(x))=3^{2x}+1=9^x+1$ The domain of both $(f \circ g) (x)$ and $(g \circ f)(x)$ is $(-\infty,\infty)$