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Chapter 5: Q. 55 (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+4x鈮�0

Short Answer

Expert verified

The inverse of the function is f-1(x)=x-4.

Step by step solution

01

Step 1. Given information :

The given function is one-to-one function.

f(x)=x2+4x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+4

Interchanging the variables x, y,

x=y2+4y2=x-4y=x-4

So, the inverse f-1(x)=x-4

03

Step 3. Check the solution :

To check whether the function is inverses are not,

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

localid="1647508144689" f(x-4)=xwegot,f-1(x)=x-4(x-4)2+4=xgiven,f(x)=x2+4x-4+4=xx=x

Similarly, f-1(fx)=x

localid="1647509050463" f-1(x2+4)=xgiven,f(x)=x2+4(x2+4)-4=x,f-1(x)=x-4x2=x|x|=x,f-1(x)=[0,鈭�)henceproved.

04

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

Graph ;

Domain of f= range off-1=[4,鈭�)

Domain of f-1= range of f=[4,鈭�)

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