Question

If f(x)=x+1/x-1

then prove that f(f(x)) = x

Answer 1

Answer:

Given f(x)=  

x+1

x−1

​

 

 

Replace x by  

x

1

​

, we get,

f(  

x

1

​

)=  

x

1

​

+1

x

1

​

−1

​

 

∴f(  

x

1

​

)=  

x

1+x

​

 

x

1−x

​

 

​

 

∴f(  

x

1

​

)=  

1+x

1−x

​

 

∴f(  

x

1

​

)=  

x+1

−(x−1)

​

 

∴f(  

x

1

​

)=−(  

x+1

x−1

​

)

∴f(  

x

1

​

)=−f(x)

Step-by-step explanation:

Answer 2

Answer:

Given f (x) = x - 1/x + 1

Replace x by 1/x , we get ,

f (1/x) = (1/x - 1) (1/x + 1)

∴ f (1/x) = 1 - x/x/1 + x/x

∴ f (1/x) = 1 - x/ 1 + x

∴ f (1/x) = -(x - 1)/x + 1

∴ f (1/x) = (x - 1)/x + 1)