# A formula and domain for inverse function and interpret the meaning of inverse function.

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter 1.6, Problem 19E
To determine

## To find: A formula and domain for inverse function and interpret the meaning of inverse function.

Expert Solution

The inverse function is, f1(c)=95C+32 , which represents the Fahrenheit temperature as a function of the Celsius temperature.

The domain of the inverse function is [273.15,] .

### Explanation of Solution

Given:

The Celsius temperature as a function of the Fahrenheit temperature is C=59(F32),F459.67 .

Calculation:

Solve the Celsius temperature function for F.

C=59(F32)95C=F3295C+32=F

Thus, the inverse function is, f1(c)=95C+32 , which represents the Fahrenheit temperature as a function of the Celsius temperature.

It is known that the range of a function is the domain of its inverse function.

So, first find the range of the given function.

Since the function is defined when F459.67 , the domain is [459.67,] .

Substitute the end points of domain for F in the given function and find its range as follows.

C=59(459.6732)=273.15C=59(32)=

Thus, the range of the given function is, [273.15,] .

Therefore, the domain of the inverse function is, [273.15,] .

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