# The inverse of a function m = f ( v ) = m 0 1 − v 2 c 2 and interpret the meaning.

### 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 20E
To determine

## To find: The inverse of a function m=f(v)=m01−v2c2 and interpret the meaning.

Expert Solution

The inverse function, f1(m)=c1m02m2 . It represents the velocity of the particle.

### Explanation of Solution

Let the given function is m=m01v2c2 .

Solve this equation for v as follows.

1v2c2=m0m1v2c2=m02m2[squaring on both sides]v2c2=1m02m2v2=c2(1m02m2)

Therefore, the value of v=c2(1m02m2) . That is, v=c1m02m2 .

Hence, the function expressed in terms of m.

Thus, the required inverse function is v=f1(m)=c1m02m2 , which represents the velocity of the particle.

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