Question

1.2 homework - graphing functions, compositior
score: 50/80 answered: 6/8
question 7
evaluate (f ∘ g)(x)
f(x) = x² + 3x
g(x) = x - 4
(f ∘ g)(x) =
question help: video

Explanation:

Step1: Recall function composition

The composition \((f \circ g)(x)\) means \(f(g(x))\). So we substitute \(g(x)\) into \(f(x)\).
Given \(f(x) = x^2 + 3x\) and \(g(x)=x - 4\), we replace every \(x\) in \(f(x)\) with \(g(x)=x - 4\).

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

\[

$$\begin{align*} f(g(x))&=(x - 4)^2+3(x - 4)\\ &=(x^2-8x + 16)+(3x-12)\\ &=x^2-8x + 16+3x-12\\ &=x^2-5x + 4 \end{align*}$$

\]

Answer:

\(x^2 - 5x + 4\)