Question

let $f(x) = -x^2 - 5$ and $g(x) = 3x + 2$.
find and simplify $(g \circ f)(x)$.
$(g \circ f)(x) = -9x^2 - 12x - 9$
$(g \circ f)(x) = -3x^2 - 13$
$(g \circ f)(x) = -3x^3 - 15x + 2$
$(g \circ f)(x) = 9x^2 + 12x - 1$

Explanation:

Step1: Define composite function

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

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

$g(f(x)) = 3(-x^2 - 5) + 2$

Step3: Distribute the 3

$= -3x^2 - 15 + 2$

Step4: Combine constant terms

$= -3x^2 - 13$

Answer:

B. $(g \circ f)(x) = -3x^2 - 13$