Question

Study the equations:

f(x)=11x-5

g(x)=-2x-4

What is h(x) = f(x) g(x)

Answer 1

`h(x)=-22x^2-34x+20`

Explanation:

Given functions:

`\begin{cases}f(x)=11x-5\\g(x)=-2x-4\end{cases}`

Function composition is an operation that takes two functions and produces a third function.

Therefore, the given composite function f(x)g(x) means to multiply the function g(x) by the function f(x):

`\begin{aligned}\implies h(x)&=f(x)g(x)\\& = (11x-5)(-2x-4)\\&=11x(-2x-4)-5(-2x-4)\\&=11x(-2x)+11x(-4)-5(-2x)-5(-4)\\&=-22x^2-44x+10x+20\\&=-22x^2-34x+20\end{aligned}`

Therefore:

`\boxed{h(x)=-22x^2-34x+20}`