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Chapter 10: Q. 56 (page 1005)

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

fx=x+8,x鈮�鈭�8

Short Answer

Expert verified

The inverse of the given function isf-1x=x2-8

Step by step solution

01

Step 1. Given information   

The given function isfx=x+8

02

Step 2. Interchange the variable y and x

Substituting fx=y, we get:

y=x+8

interchanging the variable xand y, we get:

x=y+8

03

Step 3.  Solve for y

Solving for y, we get:

x=y+8x2=y+8y=x2-8

Substituting y=f-1x, we get:

f-1x=x2-8

04

Step 4. verify that the functions are inverses.  

Substituting fxin f-1fx=x, we get:

f-1f(x)=xx-82+8=xx-8+8=xx=x

This is true

Substituting f-1'xin ff-1x=x

ff-1(x)=xfx2-8=xx2-8+8=xx=x

This is true,

Thus, the obtained inverse is correct.

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