QuestionFind the value of $g(-2)$ given $f(x)=2 x+4$ , $g(x)=-4 x^{2}-4 x-2$ , and $h(x)=-2 x^{2}+4$ .

Studdy Solution

STEP 1

Assumptions1. The function $f(x)$ is defined as $f(x)=x+4$ . The function $g(x)$ is defined as $g(x)=-4x^{}-4x-$
3. The function $h(x)$ is defined as $h(x)=-x^{}+4$
4. We are asked to find the value of $g(-)$

STEP 2

To find $g(-2)$ , we need to substitute $-2$ for $x$ in the equation for $g(x)$ .
$g(-2) = -4(-2)^{2}-4(-2)-2$

STEP 3

First, calculate the value of $(-2)^{2}$ .
$(-2)^{2} =$ So, the equation becomes $g(-2) = -()-(-2)-2$

STEP 4

Next, calculate the multiplication $-4(4)$ and $-4(-2)$ .
$-4(4) = -16$ $-4(-2) =8$ So, the equation becomes $g(-2) = -16 +8 -2$

STEP 5

Finally, calculate the sum $-16 +8 -2$ .
$-16 +8 -2 = -10$ So, $g(-2) = -10$ .

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