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)=77 d. (g ∘ f)(4)=□

Explanation:

Step1: Recall the formula for function - composition

The composition \((g\circ f)(x)=g(f(x))\). Given \(f(x) = 7x\) and \(g(x)=x + 7\).

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

First, find \(f(4)\). Since \(f(x)=7x\), then \(f(4)=7\times4 = 28\).

Step3: Substitute the result of \(f(4)\) into \(g(x)\)

Now, find \(g(f(4))\). Since \(g(x)=x + 7\) and \(f(4)=28\), then \(g(f(4))=g(28)=28 + 7=35\).

Answer:

35