Question

for f(x)=7x and g(x)=x + 7, find the following functions. a. (f ∘ g)(x); b. (g ∘ f)(x); c. (f ∘ g)(4); d. (g ∘ f)(4) a. (f ∘ g)(x)=7x + 49 (simplify your answer.) b. (g ∘ f)(x)= (simplify your answer.)

Explanation:

Step1: Recall composition of functions

The composition $(g\circ f)(x)=g(f(x))$.

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

Given $f(x) = 7x$ and $g(x)=x + 7$, then $g(f(x))=g(7x)$.
Replace $x$ in $g(x)$ with $7x$: $g(7x)=7x+7$.

Answer:

$7x + 7$