Question

question
express your answer as a polynomial in standard form.
$f(x) = -x - 5$
$g(x) = x^2 - 6x + 13$
find: $(f \circ g)(x)$

Explanation:

Step1: Substitute $g(x)$ into $f(x)$

$(f \circ g)(x) = f(g(x)) = -(g(x)) - 5$

Step2: Insert $g(x)$ expression

$(f \circ g)(x) = -(x^2 - 6x + 13) - 5$

Step3: Distribute the negative sign

$(f \circ g)(x) = -x^2 + 6x - 13 - 5$

Step4: Combine constant terms

$(f \circ g)(x) = -x^2 + 6x - 18$

Answer:

$-x^2 + 6x - 18$