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 72E

a.

To determine

To find: The inverse function of f(x)=212x .

Expert Solution

Answer to Problem 72E

  f1(x)=42x

Explanation of Solution

Given information: f(x)=212x

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 f(x) with y ,

Then,

  f(x)=212xy=212xy=4x22y=4x2y4=xx=42yf1(y)=42yf1(x)=42x

Thus, f1(x)=42x .

b.

To determine

To sketch: The graph of the function f(x)=212x and the inverse function.

Expert Solution

Explanation of Solution

Given information: f(x)=212x and f1(x)=42x

Graph:

    x02424
    f(x)21034

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 2.7, Problem 72E

Interpretation:

A point on the graph of f(x) , (0,2) . The dotted line is the graph of y=x , CD is the graph of f1(x) . AB is the perpendicular on the dotted line from the point (0,2) , It intersects the CD line at point F (2,0) .

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

Thus, it means f(x) and f1(x) is the reflection of each other in the line y=x (Dotted line).

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