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Chapter 5: Q. 98 (page 271)

Can a one-to-one function and its inverse be equal? What must be true about the graph of f for this to happen? Give some examples to support your conclusion.

Short Answer

Expert verified

Yes, a one-to-one function and its inverse are equal to each other. For this, the given function and its inverse must be symmetric about the line y=x

Example:

f=4,4,6,6,8,8,12,12f-1=4,4,6,6,8,8,12,12

Step by step solution

01

Step 1. Explanation

Yes, a one-to-one function and its inverse are equal to each other. For this, the given function and its inverse must be symmetric about the liney=x

02

Step 2. Examples

Let's take an example:

f=4,4,6,6,8,8,12,12

The inverse of the function is :

f-1=4,4,6,6,8,8,12,12

As we can see that both are same.

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