Answered

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If [tex]f(x) = 8 - 10x[/tex] and [tex]g(x) = 5x + 4[/tex], what is the value of [tex](f \cdot g)(-2)[/tex]?

A. [tex]\(-196\)[/tex]
B. [tex]\(-168\)[/tex]
C. 22
D. 78

Sagot :

GinnyAnsweridn
Sure, let's solve this step-by-step.

Given functions:
[tex]\[ f(x) = 8 - 10x \][/tex]
[tex]\[ g(x) = 5x + 4 \][/tex]

We need to determine the value of [tex]\((f \cdot g)(-2)\)[/tex].

First, let's compute [tex]\( f(-2) \)[/tex]:

[tex]\[ f(-2) = 8 - 10(-2) \][/tex]
[tex]\[ f(-2) = 8 + 20 \][/tex]
[tex]\[ f(-2) = 28 \][/tex]

Next, let's compute [tex]\( g(-2) \)[/tex]:

[tex]\[ g(-2) = 5(-2) + 4 \][/tex]
[tex]\[ g(-2) = -10 + 4 \][/tex]
[tex]\[ g(-2) = -6 \][/tex]

Now, [tex]\((f \cdot g)(-2)\)[/tex] is the product of [tex]\( f(-2) \)[/tex] and [tex]\( g(-2) \)[/tex]:

[tex]\[ (f \cdot g)(-2) = f(-2) \cdot g(-2) \][/tex]
[tex]\[ (f \cdot g)(-2) = 28 \cdot (-6) \][/tex]
[tex]\[ (f \cdot g)(-2) = -168 \][/tex]

So, the value of [tex]\((f \cdot g)(-2)\)[/tex] is [tex]\( -168 \)[/tex].

Therefore, the correct answer is:
[tex]\[ \boxed{-168} \][/tex]
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