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Chapter 5: Q. 56 (page 269)

The function fis one-to-one. Find its inverse and check your answer. Graph f,f-1 and y = x on the same coordinate axes.

f(x)=x2+9x鈮�0

Short Answer

Expert verified

The inverse of the function isf-1(x)=x-9

Step by step solution

01

Step 1. Given information :

The given function is one-to-one function.

f(x)=x2+9x鈮�0

02

Step 2. Finding the inverse of the function : 

For finding the inverse of the function we need to interchange the variables.

let, f(x)=y=x2+9

Interchanging the variables x, y,

x=y2+9y2=x-9y=x-9

So, the inverse f-1(x)=x-9

03

Step 3. Check the solution :

To check whether the function is inverses are not,

let, f(f-1(x))=x

f(x-9)=xwegot,f-1(x)=x-9(x-9)2+9=xgiven,f(x)=x2+9x-9+9=xx=x

Similarly, f-1(f(x))=x

f-1(x2+9)=xgiven,f(x)=x2+9(x2+9)-9=x,f-1(x)=x-9x2=x|x|=x,f-1(x)=[0,鈭�)henceproved.

04

Step 4. Graph representation of f, f-1 and y=x

Graph ;

Domain of f= range of f-1=[9,鈭�)

Domain of f-1= range of f=[9,鈭�)

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