Question

Let f(x) = -4x - 2 and g(x) = 5x - 6. Find fog and state its domain.

Answer 1

`\begin{gathered} f(x)=-4x-2 \\ g(x)=5x-6 \end{gathered}`
`\begin{gathered} (f_{\text{ }}\cdot g)(x)=f(x)\cdot g(x)=(-4x-2)(5x-6) \\ (f_{\text{ }}\cdot g)(x)=f(x)\cdot g(x)=-20x^2+24x-10x+12 \\ (f_{\text{ }}\cdot g)(x)=f(x)\cdot g(x)=-20x^2+14x+12 \end{gathered}`

Since the function doesn't have any restriction, the domain is:

`D\colon(-\infty,\infty)`

or all real numbers