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 90RE
To determine

To find: The inverse of the function

  f(x)=1+5x2

Expert Solution

Answer to Problem 90RE

  f1(x)=(x1)5+2

Explanation of Solution

Given information:

  f(x)=1+5x2

Calculation:

To find the inverse of a function we must prove that the function is one to one and then put function equal to y and then swap the values of x & y.

To prove that the function is one to one. Let us assume ‘a’ & ‘b’ 2 real numbers such that

  f(a)=f(b)f(a)=1+5a2f(b)=1+5b2

If

  f(a)=f(b)1+5a2=1+5b2a2=b2a=b

  The function is one to one function

  y=f(x)y=1+5x2

Swap 'x'&'y'

  x=1+5y2y2=(x1)5y=(x1)5+2

Or f1(x)=(x1)5+2 which is required inverse of given function.

We can calculate inverse of a function for one to one function only. We can also verify f1(x)

by checking that (fof1)(x)=x and (f1of)(x)=x

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