Question

express your answer as a polynomial in standard form.
$f(x) = x - 4$
$g(x) = 3x^2 + 6x + 9$
find: $(f \circ g)(x)$

Explanation:

Step1: Recall composition of functions

The composition \((f \circ g)(x)\) means \(f(g(x))\). So we substitute \(g(x)\) into \(f(x)\).

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

Given \(f(x)=x - 4\) and \(g(x)=3x^{2}+6x + 9\), then \(f(g(x))=f(3x^{2}+6x + 9)\).
Substitute \(3x^{2}+6x + 9\) for \(x\) in \(f(x)\): \(f(3x^{2}+6x + 9)=(3x^{2}+6x + 9)-4\).

Step3: Simplify the expression

Simplify \((3x^{2}+6x + 9)-4\) by combining like terms: \(3x^{2}+6x+(9 - 4)=3x^{2}+6x + 5\).

Answer:

\(3x^{2}+6x + 5\)