D − 1 and define what D − 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 84E

a.

To determine

To find: D−1 and define what D−1 represents.

Expert Solution

D1(d)=150d3

D1(d) Represents the price which is corresponding to the demand (d) of a certain commodity.

Explanation of Solution

Given information:

The demand D for a certain commodity is a function of the price given by D(p)=3p+150

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:

D(p)=3p+150d=3p+1503p=150dp=150d3D1(d)=150d3

D1(d) Represents the price which is corresponding to the demand (d) of a certain commodity.

b.

To determine

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

Expert Solution

D1(30)=40

D1(30)Represents the price is 40 when the demand is 30 for a certain commodity.

Explanation of Solution

Given information:

The demand D for a certain commodity is a function of the price given by D(p)=3p+150

D1(d)=150d3

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:

D1(30)=150303=1203=40

D1(30)Represents the price is 40 when the demand is 30 for a certain commodity.

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