if (f(x)=8 - 10x) and (g(x)=5x + 4), what is the value of ((fg)(-2))?\n-196\n-168\n22\n78

Explanation:

Step1: Define the product - function

The product of two functions $(fg)(x)=f(x)\times g(x)$. Given $f(x) = 8 - 10x$ and $g(x)=5x + 4$, then $(fg)(x)=(8 - 10x)(5x + 4)$.

Step2: Expand the product

Using the FOIL method: [ \begin{align*} (8 - 10x)(5x + 4)&=8\times(5x)+8\times4-10x\times(5x)-10x\times4\ &=40x + 32-50x^{2}-40x\ &=- 50x^{2}+32 \end{align*} ]

Step3: Substitute $x = - 2$

Substitute $x=-2$ into $(fg)(x)=-50x^{2}+32$. [ \begin{align*} (fg)(-2)&=-50\times(-2)^{2}+32\ &=-50\times4 + 32\ &=-200+32\ &=-168 \end{align*} ]

Answer:

-168