BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 1.6, Problem 58E

(a)

To determine

To find : The expression for g1(x)

Expert Solution

Explanation of Solution

Given: The given function is g(x)=x6+x40 .

Consider the function.

  g(x)=x6+x40

To get the inverse replace the x with y and vice-versa in the given function.

  x=y6+y4

With the help of CAS the solution obtained is,

  y=±13(3327x24x+27x2323+233327x24x+27x23)13

Also,

  y=±((1i3)3327x24x+27x23623+(1+i3)3×22/33327x24x+27x23)13

And,

  y=±((1+i3)3327x24x+27x23623+(1i3)3×22/33327x24x+27x23)13

The four different solutions are not valid because they contain i that makes them non-rea; solutions

Therefore, the inverse function is g1(x)=±13(3327x24x+27x2323+233327x24x+27x23)13 .

(b)

To determine

To graph : The function y=g(x),y=x and y=g1(x) .

Expert Solution

Explanation of Solution

Given: The given function is g(x)=x6+x40 .

The graph of y=g(x),y=x and y=g1(x) is shown below.

  Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 1.6, Problem 58E

Figure (1)

It is visible from the figure, that the two graphs are symmetric about the line y=x .

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