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 56E
To determine

To find the inverse function of f where f(x)=(2x3)5 .

Expert Solution

Answer to Problem 56E

The inverse of the function f(x)=(2x3)5 is f1(x)=2x53

Explanation of Solution

Given information: A function f(x)=(2x3)5

Calculation: Put f(x)=y

   f(x)= (2 x 3 ) 5 y= (2 x 3 ) 5

Now solve for x.

   y= (2 x 3 ) 5 y5=2x3x3=2y5x=2y53

Now, interchange x and y.

  y=2x53

Therefore, the inverse function is

  f1(x)=2x53

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