Q 281 - Intermediate Algebra

Question

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

Step-by-Step Solution

Answer

The solution is (a) $49x^2-64$

(b) $132$

Step 1, Given information

$f\left(x\right)=7x-8$ and $g\left(x\right)=7x+8$

Part (a) Step 1. Find f · g x

$$\begin{gathered} \left(f·g\right)\left(x\right)=f\left(x\right)·g\left(x\right) \\ \left(f·g\right)\left(x\right)=\left(7x-8\right)\left(7x+8\right) \\ \left(f·g\right)\left(x\right)=7x\left(7x+8\right)-8\left(7x+8\right) \\ \left(f·g\right)\left(x\right)=49x^2-64 \end{gathered}$$

Part (b) Step 1. Substitute x = - 2

$$\begin{gathered} \left(f·g\right)\left(x\right)=49x^2-64 \\ \left(f·g\right)\left(-2\right)=49{\left(-2\right)}^2-64 \end{gathered}$$

(b) $\left(f·g\right)\left(-2\right)=132$