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Chapter 10: Q. 46 (page 1004)

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

f(x)=7x-1

Short Answer

Expert verified

The inverse of the function isf-1(x)=x+17

Step by step solution

01

Step 1. Given data

The given function isf(x)=7x-1

02

Step 2. Substitute y for f(x)

Replace f(x)with y

role="math" localid="1644861512873" f(x)=7x-1y=7x-1

03

Step 3. Exchange x & y

Interchange variables x&y

role="math" localid="1644862399655" y=7x-1x=7y-1

04

Step 4. solve the equation for y

Add 1to both sides

x+1=7y-1+1x+1=7y

Divide both sides by 7

role="math" localid="1644864329322" x+17=7y7x+17=y

05

Step 5. Substitute f-1(x) for y

Replace ywith f-1(x)

role="math" localid="1644866128198" x+17=yx+17=f-1(x)f-1(x)=x+17

06

Step 6. verification

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

role="math" localid="1644866011663" f-1(7x-1)=?x(7x-1)+17=?x7x7=?xx=x

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

role="math" localid="1644866099623" f(x+17)=?x7(x+17)-1=?xx+1-1=?xx=x

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Most popular questions from this chapter

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