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Chapter 5: Q. 84 (page 270)

Find the inverse of the functionf(x)=r2-x20鈮�x鈮�r

Short Answer

Expert verified

The inverse of the function f(x)=r2-x20鈮�x鈮�ris f-1(x)=r2-x20鈮�x鈮�r

Step by step solution

01

Step 1. Given data 

The given function is

f(x)=r2-x20鈮�x鈮�r

02

Step 2. interchanging variables 

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

f(x)=r2-x2y=r2-x2x=r2-y2

03

Step 3. The inverse of the function 

Solve the equation for y

x=r2-y2x2=r2-y2y2=r2-x2y=r2-x2

replace ywith f-1(x)

y=r2-x2f-1(x)=r2-x2

04

Step 4. Verification 

Determine f(f-1(x))

f(f-1(x))=fr2-x2f(f-1(x))=r2-r2-x22f(f-1(x))=r2-r2+x2f(f-1(x))=x2f(f-1(x))=x

Determine f-1(f(x))

f-1(f(x))=f-1r2-x2f-1(f(x))=r2-r2-x22f-1(f(x))=r2-r2+x2f-1(f(x))=x2f-1(f(x))==x

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

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