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) $(f \circ g)(x)=\sqrt{5x - 4}$ (simplify your answer.)
the domain is $\left\frac{4}{5},\infty\
ight)$.
(type your answer in interval notation.)
(b) $(g \circ f)(x)=\square$ (simplify your answer.)

Explanation:

Step1: Recall function composition

To find \((g \circ f)(x)\), we substitute \(f(x)\) into \(g(x)\). So \(g(f(x))\) means we replace \(x\) in \(g(x) = 5x\) with \(f(x)=\sqrt{x - 4}\).

Step2: Substitute and simplify

\(g(f(x))=5\times f(x)=5\times\sqrt{x - 4}\). So \((g\circ f)(x)=5\sqrt{x - 4}\).

Answer:

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