# The inverse of a function we must prove that the function is one to one and then put function equal to y and then swap the values of ‘x’ and ‘y’. ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071 ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 2, Problem 88RE
To determine

## To find: The inverse of a function we must prove that the function is one to one and then put function equal to y and then swap the values of ‘x’ and ‘y’.

Expert Solution

The required inverse of given function is f1(x)=3x12

We can calculate inverse of a function for one to one function only.

### Explanation of Solution

Given information:

A function f(x)=2x+13

Calculation:

To prove that the function is one to one, let us assume that ‘a’ and ‘b’ are real numbers such that:

f(a) = f(b)

f(a)=2a+13f(b)=2b+13

If f(a) = f(b)

2a+13=2b+132a+1=2b+1a=b

Therefore, the function is one to one function,

y=f(x)y=2x+13swap'x'and'y'x=2y+133x=2y+1y=3x12

Or f1(x)=3x12 which is required inverse of given function.

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