Chapter 1.6, Problem 107E

a.

To determine

To graph the function using graphing device.

Explanation of Solution

Given information : Use graphing device to graph the function $f\left(x\right)=x^3+x+1$.

Graph : Sketch the graph using graphing utility.

Step 1: Press WINDOW button to access the Window editor.

Step 2: Press $\boxed{\text{Y=}}$ button.

Step 3: Enter the expression $x^3+x+1$ which is required to graph.

Step 4: Press GRAPH button to graph the function.

The graph is obtained as:

  

Interpretation :

From the above graph, it can be observed that the domain of $f$ is $ℝ$.

b.

To determine

To graph: the inverse function of $f$ by using the inverse feature of the function of graphing utility.

Explanation of Solution

Given information :

The function is $f\left(x\right)=x^3+x+1$.

Graph : the graph of the inverse function of a function is the reflection in the line of $y=x$ ,

Thus, the graph can be obtained as:

  

Interpretation: from the above graph it can be observed that the graph of function and inverse function are reflection of each other in the line of $y=x$.

c.

To determine

To state : that whether the inverse relation is an inverse function or not.

Answer to Problem 107E

Yes, the inverse relation is an inverse function.

Explanation of Solution

Given information :

The function is $f\left(x\right)=x^3+x+1$.

from the above graph shown in part (b) it can be observed that the graph of inverse function does not have any vertical line that intercept the graph more than one time, so the inverse function satisfy the vertical test.

So inverse relation is an inverse function or not.