Composition of Functions · Exercise 25

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

Given $f\left(x\right)=\frac{1}{x}$ and $g\left(x\right)=x-3,$ find the following:

ⓐ $\left(f\circ g\right)\left(x\right)$
ⓑthe domain of $\left(f\circ g\right)\left(x\right)$ in interval notation
ⓒ $\left(g\circ f\right)\left(x\right)$
ⓓthe domain of $\left(g\circ f\right)\left(x\right)$
ⓔ $\left(\frac{f}{g}\right)\left(x\right)$

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 25