Question

Set of the following functions. Find (f•g)(-9) Simplify your answer.

Answer 1

First, solve for (f • g)(x)

`\begin{gathered} \text{Given:} \\ f(x)=x^2+7 \\ g(x)=-x+4 \\ \\ (f\cdot g)(x)=f(x)\cdot g(x) \\ (f\cdot g)(x)=(x^2+7)(-x+4) \\ (f\cdot g)(x)=(x^2)(-x)+(x^2)(4)+(7)(-x)+(7)(4) \\ (f\cdot g)(x)=-x^3+4x^2-7x+28 \end{gathered}`

Not that we have (f • g)(x), we solve for (f • g)(-9)

`\begin{gathered} (f\cdot g)(x)=-x^3+4x^2-7x+28 \\ (f\cdot g)(-9)=-(-9)^3+4(-9)^2-7(-9)+28 \\ (f\cdot g)(-9)=-(-729)^{}+4(81)+63+28 \\ (f\cdot g)(-9)=729^{}+324+63+28 \\ (f\cdot g)(-9)=1144 \end{gathered}`