Question

Find (f • g)(4) for the following functions.f(x) = -x - 1 and g(x) = x^3 + x^2

Answer 1

`\begin{gathered} \text{Solve first for }(f\cdot g)(x) \\ f(x)=-x-1 \\ g(x)=x^3+x^2 \\ (f\cdot g)(x)=f(x)\cdot g(x) \\ (f\cdot g)(x)=(-x-1)\cdot(x^3+x^2) \\ (f\cdot g)(x)=(-x)(x^3_{})+(-x)(x^2)+(-1)(x^3)+(-1)(x^2) \\ (f\cdot g)(x)=-x^4-x^3-x^3-x^2 \\ (f\cdot g)(x)=-x^4-2x^3-x^2 \\ \text{Then solve for }(f\cdot g)(4) \\ (f\cdot g)(x)=-x^4-2x^3-x^2 \\ (f\cdot g)(4)=-(4)^4-2(4)^3-(4)^2 \\ (f\cdot g)(4)=-256-2(64)-16 \\ (f\cdot g)(4)=-256-128-16 \\ (f\cdot g)(4)=-400\text{ final answer} \end{gathered}`