Question

for the functions $f(x) = \sqrt{x - 4}$ and $g(x) = 5x$ find the following.
(a) $(f \circ g)(x)$ and its domain
(b) $(g \circ f)(x)$ and its domain

(a) $(f \circ g)(x) = \square$ (simplify your answer.)

Explanation:

Step1: Recall composition of functions

The composition \((f \circ g)(x)\) means \(f(g(x))\). So we substitute \(g(x)\) into \(f(x)\).

Step2: Substitute \(g(x)\) into \(f(x)\)

Given \(f(x)=\sqrt{x - 4}\) and \(g(x)=5x\), substitute \(g(x)\) (which is \(5x\)) into the \(x\) of \(f(x)\). So we get \(f(g(x))=\sqrt{(5x)-4}=\sqrt{5x - 4}\).

Answer:

\(\sqrt{5x - 4}\)