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)=7x + 7 (simplify your answer.) c. (f ∘ g)(4)=□

Explanation:

Step1: Recall the formula for function - composition

The composition of functions \((f\circ g)(x)=f(g(x))\) and \((g\circ f)(x)=g(f(x))\). We already know that \((f\circ g)(x) = 7x + 49\) from part a.

Step2: Substitute \(x = 4\) into \((f\circ g)(x)\)

Substitute \(x = 4\) into the function \((f\circ g)(x)=7x + 49\). So \((f\circ g)(4)=7\times4+49\).

Step3: Calculate the value

First, calculate \(7\times4 = 28\). Then \(28+49=77\).

Answer:

77