Question

express your answer as a polynomial in standard form.
$f(x) = x - 4$
$g(x) = 2x^2 + 2x + 14$
find: $(f \circ g)(x)$

Explanation:

Step1: Define composite function

$(f \circ g)(x) = f(g(x))$

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

$f(g(x)) = f(2x^2 + 2x + 14)$

Step3: Replace $x$ in $f(x)$

$f(2x^2 + 2x + 14) = (2x^2 + 2x + 14) - 4$

Step4: Simplify the expression

$2x^2 + 2x + 14 - 4 = 2x^2 + 2x + 10$

Answer:

$2x^2 + 2x + 10$