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Chapter 10: Q. 41 (page 1004)

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

f(x)=9x

Short Answer

Expert verified

The inverse of the functionf(x)=9xis

localid="1644857079934" f-1(x)=x9

Step by step solution

01

Step 1. Given data

The given function isf(x)=9x

02

Step 2. Substitute y for f(x)

Replacef(x)with y

f(x)=9xy=9x

03

Step 3. Exchange x & y

Replace xwith yand ywith x

y=9xx=9y

04

Step 4. solve the equation for y

Divide both sides of the equation by 9

x9=9y9x9=y

05

Step 5. Substitute f-1(x) for y

Replace ywith f-1(x)

x9=yx9=f-1(x)f-1(x)=x9

06

Step 6. verification

Show f-1(f(x))=x

f-1(f(x))=?xf-1(9x)=?x9x9=?xx=x

Show f(f-1(x))=x

f(f-1(x))=?xf(x9)=?x9(x9)=?xx=x

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