Chapter 1.5, Problem 24E

To determine

To evaluate the indicated function for $f\left(x\right)=x^2-1$ and $g\left(x\right)=x-2$ . And, verify the result using graphing utility, if possible.

Answer to Problem 24E

  $\left(f\cdot g\right)\left(4\right)=30$

Explanation of Solution

Given:

The functions $f\left(x\right)=x^2-1$ and $g\left(x\right)=x-2$ .

Calculation:

  $\begin{array}{c}\left(f\cdot g\right)\left(x\right)=\left(x^2-1\right)\left(x-2\right)\\ =x^{2}x-2x^2-1\cdot x+1\cdot 2\\ =x^3-2x^2-x+2\end{array}$

Now, substitute $x=4$ in the above function.

  $\begin{array}{c}\left(f\cdot g\right)\left(4\right)={\left(4\right)}^3-2{\left(4\right)}^2-\left(4\right)+2\\ =64-2\left(16\right)-4+2\\ =64-32-4+2\\ =30\end{array}$

Therefore, $\left(f\cdot g\right)\left(4\right)=30$ .

Verification:

Use the graphing utility to graph the function as shown below.

  

From the graph it can be observed that $\left(f\cdot g\right)\left(4\right)=30$ .