QuestionEvaluate $(h \cdot g)(-4)$ for the functions $f(x)=-6x$ , $g(x)=|x+7|$ , and $h(x)=\frac{1}{x+5}$ .

Studdy Solution

STEP 1

Assumptions1. We are given three functions $f(x)=-6x$ , $g(x)=|x+7|$ , and $h(x)=\frac{1}{x+5}$ . . We are asked to evaluate the function $(h \cdot g)(-4)$ , which means we need to evaluate the function $h(x)$ at the value given by $g(-4)$ .

STEP 2

First, we need to evaluate the function $g(x)$ at $x=-4$ . $g(-4) = |-4+7|$

STEP 3

Calculate the value of $g(-)$ .
$g(-) = |-+7| = |3| =3$

STEP 4

Now that we have the value of $g(-4)$ , we can substitute this into the function $h(x)$ to find $(h \cdot g)(-4)$ .
$h(g(-4)) = h(3) = \frac{1}{3+}$

STEP 5

Calculate the value of $h(3)$ .
$h(3) = \frac{1}{3+5} = \frac{1}{8}$ The value of the function $(h \cdot g)(-4)$ is $\frac{1}{8}$ .

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