# To rearrange the expression c = f ( x ) − f ( a ) x − a and conclude that f is a linear function.

### 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 2.4, Problem 33E
To determine

## To rearrange the expression c=f(x)−f(a)x−a       and conclude that f is a linear function.

Expert Solution

Linear function is f(x)=mx+b .In this case, we have m=c and b=f(a)ca .

So, this function is linear

### Explanation of Solution

Given information:

The expression is c=f(x)f(a)xa       and rearrange it into f(x)=cx+(f(a)ca)

c=f(x)f(a)xac(xa)=f(x)f(a)                      [multiply by xa]c(xa)+f(a)=f(x)f(x)=cx+(f(a)ca)

Linear function is f(x)=mx+b .In this case, we have m=c and b=f(a)ca .

So, this function is linear.

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