Chapter 1.5, Problem 21E

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 21E

  $\left(f-g\right)\left(0\right)=1$

Explanation of Solution

Given:

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

  $\left(f-g\right)\left(0\right)$ .

Calculation:

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

Now, substitute $x=0$ in the above function.

  $\begin{array}{c}\left(f-g\right)\left(0\right)={\left(0\right)}^2-\left(0\right)+1\\ =0+0+1\\ =1\end{array}$

Therefore, $\left(f-g\right)\left(0\right)=1$ .

Verification:

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

  

From the graph it can be observed that $\left(f-g\right)\left(0\right)=1$ .