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 74E

a.

To determine

To find: The inverse function of g(x)=x2+1 , x0

Expert Solution

Answer to Problem 74E

  g1(x)=x1

Explanation of Solution

Given information: g(x)=x2+1 , x0

Concept Use: 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 g(x) with y ,

Then,

  g(x)=x2+1y=x2+1x2=y1x=y1g1(y)=y1g1(x)=x1

Thus, g1(x)=x1 .

b.

To determine

To sketch: The graph of the function g(x)=x2+1 , x0 and the inverse function.

Expert Solution

Explanation of Solution

Given information: g(x)=x2+1 , x0 and g1(x)=x1

Graph:

    x01234
    g(x)1251017

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 2.7, Problem 74E

Interpretation:

A point on the graph of g(x) , (2,5) . The dotted line is the graph of y=x , CD is the graph of g1(x) . AB is the perpendicular on the dotted line from the point (2,5) , It intersects the CD line at point F (5,2) .

It is clear that the coordinate of E is reversed from F.

Thus, it means g(x) and g1(x) is the reflection of each other in the line y=x (Dotted line).

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