# F − 1 and define what F − 1 represents.

### 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 2.7, Problem 85E

a.

To determine

## To find: F−1 and define what F−1 represents.

Expert Solution

F1(F)=59(F32)

F1(F) Represents the equivalent value of F in the Celsius scale.

### Explanation of Solution

Given information:

The relationship between the Fahrenheit ( F ) and Celsius ( C ) scales is given by

F(C)=95C+32

Concept used: If f be a one-to-one function with domain A and range B. Then its inverse function f1 has domain B and range A and is defined by

f1(y)=x      f(x)=y

Calculation:

F(C)=95C+32F=95C+32F32=95CC=59(F32)F1(F)=59(F32)

F1(F) Represents the equivalent value of F in the Celsius scale.

b.

To determine

### To find: F−1(86) and state what it represents.

Expert Solution

F1(86)=30

The answer of F1(86) represent the equivalent value of 86 Fahrenheit in Celsius scale.

### Explanation of Solution

Given information:

Given information:

The relationship between the Fahrenheit ( F ) and Celsius ( C ) scales is given by

F(C)=95C+32

F1(F)=59(F32)

Concept Used:

If f be a one-to-one function with domain A and range B. Then its inverse function f1 has domain B and range A and is defined by

f1(y)=x      f(x)=y

Calculation:

F1(86)=59(8632)=59×54=30

The answer of F1(86) represent the equivalent value of 86 Fahrenheit in Celsius scale.

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