# V − 1 and define what V − 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 83E

a.

To determine

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

Expert Solution

v1(v)=(0.25v18500)

v1(v) Represents the distance from the central axis of a vein or artery where the velocity of the blood is v .

### Explanation of Solution

Given information:

An artery with radius 0.5cm , v (in cm/s) is given as a function of r (in cm) by

v(r)=18500(0.25r2)

r is the distance from the central axis of the artery.

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:

v(r)=18500(0.25r2)v=18500(0.25r2)v18500=0.25r2r2=0.25v18500r=(0.25v18500)v1(v)=(0.25v18500)

v1(v) Represents the distance from the central axis of a vein or artery where the velocity of the blood is v .

b.

To determine

### To find: v−1(30) and state what it means.

Expert Solution

v1(30)0.49838

v1(30) Represents the distance ( in cm ) from the central axis where the velocity of blood flow is 30cm/s .

### Explanation of Solution

Given information:

An artery with radius 0.5cm , v (in cm/s) is given as a function of r (in cm) by

v(r)=18500(0.25r2)

r is the distance from the central axis of the artery.

v1(v)=(0.25v18500)

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:

v1(30)=(0.253018500)0.49838

v1(30) Represents the distance ( in cm ) from the central axis where the velocity of blood flow is 30cm/s .

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