Composition of Functions · Exercise 28

Use each set of functions to find $f\left(g\left(h\left(x\right)\right)\right).$ Simplify your answers.

Given functions $p\left(x\right)=\frac{1}{\sqrt{x}}$ and $m\left(x\right)=x^2-4,$ state the domain of each of the following functions using interval notation:

ⓐ $\frac{p\left(x\right)}{m\left(x\right)}$
ⓑ $p\left(m\left(x\right)\right)$
ⓒ $m\left(p\left(x\right)\right)$

OpenStax, Algebra and Trigonometry 2e · §3.4 Composition of Functions · Exercise 28