QuestionFind $(g \cdot h)(-4)$ where $g(a)=2a-1$ and $h(a)=3a-3$ .

Studdy Solution

STEP 1

Assumptions1. The functions are defined as $g(a)=a-1$ and $h(a)=3a-3$ . We need to find the value of the product of these two functions, $(g \cdot h)(-4)$ , where $a=-4$

STEP 2

The product of two functions, $g$ and $h$ , at a point $a$ is given by $(g \cdot h)(a) = g(a) \cdot h(a)$ . We can use this formula to find $(g \cdot h)(-4)$ .

STEP 3

First, let's find the value of $g(-)$ by substituting $a=-$ into the function $g(a)$ .
$g(-) =2(-) -1$

STEP 4

Calculate the value of $g(-4)$ .
$g(-4) =2(-4) -1 = -8 -1 = -9$

STEP 5

Next, let's find the value of $h(-4)$ by substituting $a=-4$ into the function $h(a)$ .
$h(-4) =3(-4) -3$

STEP 6

Calculate the value of $h(-4)$ .
$h(-4) =3(-4) -3 = -12 -3 = -15$

STEP 7

Now that we have the values of $g(-4)$ and $h(-4)$ , we can find the value of $(g \cdot h)(-4)$ by multiplying these two values.
$(g \cdot h)(-4) = g(-4) \cdot h(-4)$

STEP 8

Substitute the values of $g(-4)$ and $h(-4)$ into the equation.
$(g \cdot h)(-4) = - \cdot -15$

STEP 9

Calculate the value of $(g \cdot h)(-4)$ .
$(g \cdot h)(-4) = -9 \cdot -15 =135$ So, $(g \cdot h)(-4) =135$ .

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