Question

For function $f\left(x\right)=x-7$and $g\left(x\right)=x^2+8x+4$. Find (a)$\left(f·g\right)\left(x\right)$(b)$\left(f·g\right)\left(2\right)$

Short answer

(a) $\left(f·g\right)\left(x\right)=x^3+x^2-52x-28$

(b)$\left(f·g\right)\left(2\right)=-120$

Step-by-step solution

Step 1. Given Information

Given functions $f\left(x\right)=x-7$and $g\left(x\right)=x^2+8x+4$.

We need to find$\left(f·g\right)\left(x\right)and\left(f·g\right)\left(2\right)$

Part (a) Step 1. Finding f·gx

$$\begin{gathered} \left(f·g\right)\left(x\right)=f\left(x\right)g\left(x\right)=\left(x-7\right)\left(x^2+8x+4\right) \\ \left(f·g\right)\left(x\right)=x^3+8x^2+4x-7x^2-56x-28 \\ \left(f·g\right)\left(x\right)=x^3+x^2-52x-28 \end{gathered}$$

Part (b) Step 1. Finding f·g2

$$\begin{gathered} \left(f·g\right)\left(x\right)=x^3+x^2-52x-28 \\ \left(f·g\right)\left(2\right)=2^3+2^2-52\left(2\right)-28 \\ \left(f·g\right)\left(2\right)=8+4-104-28 \\ \left(f·g\right)\left(2\right)=12-132=-120 \end{gathered}$$