Question

for the functions $f(x) = \sqrt{x - 2}$ and $g(x) = 3x$ 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 \(f(x)\).
Given \(f(x)=\sqrt{x - 2}\) and \(g(x)=3x\), substitute \(g(x)\) for \(x\) in \(f(x)\).

Step2: Substitute and simplify

\(f(g(x))=f(3x)=\sqrt{(3x)-2}=\sqrt{3x - 2}\)

Answer:

\(\sqrt{3x - 2}\)