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Chapter 5: Q. 100 (page 271)

Give an example of a function whose domain is the set of real numbers and that is neither increasing nor decreasing on its domain, but is one-to-one.

Short Answer

Expert verified

An example of a function is let f(x)=kwhere k is constant. Now, divide the domain of the function into piecewise like k is constant for 1≤x≤2. Take another function f(x)=a where ais constant for 2≤x≤3. Thus, we can divide the domain piecewise to make it one-to-one, and because the function's value is constant, it is neither increasing nor decreasing.

Step by step solution

01

Step 1. Given Information

We have to give an example of a function where the domain is the set of all real numbers and which is neither increasing nor decreasing on its domain but is one-to-one.

02

Step 2. Giving an example

An example of a function is let f(x)=k wherek is constant. Now, divide the domain of the function into piecewise like k is constant for1≤x≤2 . Take another function f(x)=awhereais constant for2≤x≤3 . Thus, we can divide the domain piecewise to make it one-to-one, and because the function's value is constant, it is neither increasing nor decreasing.

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