Question

for f(x) = \sqrt{x} and g(x) = x + 1, find the following functions. a. (f ∘ g)(x); b. (g ∘ f)(x); c. (f ∘ g)(3); d. (g ∘ f)(3)
a. (f ∘ g)(x) =
(simplify your answer.)

Explanation:

Step1: Recall composition of functions definition

The composition \((f\circ g)(x)=f(g(x))\). Given \(f(x)=\sqrt{x}\) and \(g(x)=x + 1\), we substitute \(g(x)\) into \(f(x)\).

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

\(f(g(x))=f(x + 1)=\sqrt{x+1}\)

Answer:

\(\sqrt{x + 1}\)