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, Problem 91RE

a.

To determine

To draw: Graph of the function

Expert Solution

Explanation of Solution

Given information:

  f(x)=x24    x0

Graph : To draw the graph of f1 if the f(x) is given then switch all the x and y values in each point to graph the inverse. Just look at those values switching places from the f(x) function to its inverse g(x) reflected over the line y=x

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 2, Problem 91RE , additional homework tip  1

Interpretation :

The values switching places from the f(x) function to its inverse g(x) are reflected over the line y=x

b.

To determine

To draw: Inverse of function by using graph from part (a).

Expert Solution

Explanation of Solution

Given information:

  f(x)=x24    x0

Graph: To draw the graph of f1 if the f(x) is given then switch all the x and y values in each point to graph the inverse. Following is the graph of f1 .

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 2, Problem 91RE , additional homework tip  2

Interpretation :

The values switching places from the f(x) function to its inverse g(x) reflected over the line y=x

c.

To determine

To find: The equation for f1 .

Expert Solution

Answer to Problem 91RE

   f1(x)=x+4

Explanation of Solution

Given information:

  f(x)=x24    x0

Calculation:

To find the equation for f1

  

  y=f(x)y=x24

Swap ‘x’ with ‘y’

  x=y24

  y2=x+4y=x+4   f1(x)=x+4

is the required equation.

After swapping the values of x and y, solve the equation for y by bringing like terms together and the final value of y is the inverse of the function i.e. f1(x) .

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