Composition of Functions · Exercise 29

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

Given functions $q\left(x\right)=\frac{1}{\sqrt{x}}$ and $h\left(x\right)=x^2-9,$ state the domain of each of the following functions using interval notation.

ⓐ $\frac{q\left(x\right)}{h\left(x\right)}$
ⓑ $q\left(h\left(x\right)\right)$
ⓒ $h\left(q\left(x\right)\right)$

Its source prints no answer for this problem, so there's nothing to check against.

OpenStax, Algebra and Trigonometry 2e · §3.4 Composition of Functions · Exercise 29