Chapter 1.6, Problem 57E

To determine

To state: that whether the function is one-to-one or not and verify graphically.

Answer to Problem 57E

No, the function is not one-to-one.

Explanation of Solution

Given information : thefunction is,

  $\begin{array}{l}f\left(x\right)=x^4\\ \end{array}$

let $f\left(x\right)=f\left(y\right)$ ,

  $\begin{array}{l}f\left(x\right)=f\left(y\right)\\ x^4=y^4\text{ [substitute }f\left(x\right)=x^4]\\ x\ne y\end{array}$

There is many possibilities that $x\text{ and }y$ , are not equal. So the value of y has occur more than one time for x -value. So the function is not one-to-one.

to graph the given function first create a table for plotting the points and then make a curve smoothly by jointing the points.

x	y
0	0
2	16
1	1
-1	1

The graph can be obtained as:

  

From the above graph, it can be observed that the graph of the function hashorizontal lines that intercept the graph more than one times, so the function isnot a one-to-one and its inverse functiondoes not exists.