BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 2.7, Problem 64E

a.

To determine

To sketch: The graph of the function f(x)=x31 .

Expert Solution

Explanation of Solution

Given information:

  f(x)=x31

Graph:

    x01212
    f(x)10729

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 2.7, Problem 64E , additional homework tip  1

Interpretation: The graph is the function for f(x)=x31 .

b.

To determine

To sketch: The graph of f1 using the graph of f

Expert Solution

Explanation of Solution

Given information:

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 2.7, Problem 64E , additional homework tip  2

Graph:

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 2.7, Problem 64E , additional homework tip  3

Interpretation:

Line M is the graph of function f . Line N is the graph of function y=x . After reflecting the line M in line N, we get line M' . Therefore, M' is the graph of function f1 .

c.

To determine

To find: The inverse function of f .

Expert Solution

Answer to Problem 64E

  f1(x)=x+13

Explanation of Solution

Given information: f(x)=x31 .

Concept used: Let, 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 defining by f1(y)=xf(x)=y for any y in B.

Calculation:

First, we replace f(x) with y ,

Then,

  f(x)=x31y=x31y+1=x3x=y+13f1(y)=y+13f1(x)=x+13

Thus, f1(x)=x+13 .

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