Chapter 1.6, Problem 10QR

To determine

To find: One way to restrict the domain of the given function such that the resulting function is one to one.

Answer to Problem 10QR

One way to restrict the domain of the function is $x\ge 0$ such that it is one-to-one function.

Explanation of Solution

Given information:The function is $f\left(x\right)=x^4-2$ .

The graph of the function $f\left(x\right)=x^4-2$ is a U-shaped graph. By horizontal line test, line will intersect the graph at more than once.

To make the function one-to-one, either the left half or the right half part of the graph need to pass Horizontal Line Test.The vertex of the graph is at $\left(0,-2\right)$ .

So, the right half of the graph will pass the test if function is restricted to $x\ge 0$ .

Therefore,one way to restrict the domainof the function is $x\ge 0$ such that it is one-to-one function.