Question

for the functions f(x)=√(x - 1) and g(x)=5x find the following.
(a) (f ∘ g)(x) and its domain
(b) (g ∘ f)(x) and its domain
(a) (f ∘ g)(x) =
(simplify your answer.)

Explanation:

Step1: Recall function composition

Function composition \((f \circ g)(x)\) means \(f(g(x))\). So we substitute \(g(x)\) into \(f(x)\).
Given \(f(x)=\sqrt{x - 1}\) and \(g(x)=5x\), substitute \(g(x)=5x\) into \(f\): \(f(g(x))=f(5x)=\sqrt{(5x)-1}\).

Step2: Simplify the expression

The expression \(\sqrt{5x - 1}\) is already simplified as there are no like terms to combine or further factoring that simplifies the square - root expression.

Answer:

\(\sqrt{5x - 1}\)