Question

given the following functions f(x) and g(x), solve for (f · g)(2) and select the correct answer below: f(x)=3x^{2}+2 g(x)=x - 8 -84 84 42 -42

Explanation:

Step1: Find f(2)

Substitute x = 2 into f(x):
$f(2)=3\times2^{2}+2=3\times4 + 2=12 + 2=14$

Step2: Find g(2)

Substitute x = 2 into g(x):
$g(2)=2 - 8=-6$

Step3: Calculate (f·g)(2)

By the definition of function - product $(f\cdot g)(x)=f(x)\cdot g(x)$, so $(f\cdot g)(2)=f(2)\cdot g(2)$.
$(f\cdot g)(2)=14\times(-6)=-84$

Answer:

-84