Question

Given the functions 𝑔(𝑥) = 𝑥 − 5 and 𝑓(𝑥) = 𝑒

𝑥

Determine (𝑓 ∘ 𝑔)(5)

Answer 1

Substitute $x=5$ into the expression for $g(x):$ $g(5)=5-5=0$. Then, substitute $g(5)$ into the expression for $f(x)$: $f(g(5))=f(0)=e^0=1$. Thus, $(f\circ g)(5)=1$.