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Chapter 10: Q. 55 (page 1005)

In the following exercise, find the inverse of each function.

fx=x-2,x鈮�2

Short Answer

Expert verified

The inverse of the given function isf-1x=x2+2

Step by step solution

01

Step 1. Given information  

The given function isfx=x-2,x鈮�2

02

Step 2.  Interchange the variable y and x

Substituting fx=y, we get:

y=x-2

interchanging the variable xand y, we get:

x=y-2

03

Step 3. Solve for y

Solving for y, we get:

x=y-2x2=y-2[squaringbothsides]y=x2+2

Substituting y=f-1x, we get:

role="math" localid="1644904764143" f-1x=x2+2

04

Step 4. verify that the functions are inverses. 

Substituting fxin role="math" localid="1644904451551" f-1f(x)=x, we get:

f-1f(x)=xf-1x-2=xx-22+2=xx-2+2=xx=x

This is true.

Substitutingfxin ff-1x=x, we get:

ff-1(x)=xf(x2+2)=xx2+2-2=xx2=xx=x

This is also true.

Thus, the obtained inverse is correct

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