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Chapter 5: Q. 83 (page 270)

Find the inverse of the linear functionf(x)=mx+bm鈮�0

Short Answer

Expert verified

The inverse of the functionf(x)=mx+bm鈮�0 isf-1(x)=x-bmm鈮�0

Step by step solution

01

Step 1. Given data 

The given function is

f(x)=mx+bm鈮�0

02

Step 2. interchanging variables 

Replace f(x) with y and interchange x and y

role="math" localid="1646177714686" f(x)=mx+by=mx+bx=my+b

03

Step 3. The inverse of the function 

Solve the equation for y

x=my+bx-b=myx-bm=yy=x-bm

replace ywith f-1(x)

role="math" localid="1646177950266" f-1(x)=x-bmm鈮�0

04

Step 4. Verification 

Determine f(f-1(x))

f(f-1(x))=fx-bmf(f-1(x))=mx-bm+bf(f-1(x))=x-b+bf(f-1(x))=x

Determinef-1(f(x))

f-1(f(x))=f-1(mx+b)f-1(f(x))=(mx+b)-bmf-1(f(x))=mxmf-1(f(x))=x

f-1(f(x))=x&f(f-1(x))=xso inverse function is correct

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