let f(x) be a continuous function for all x belongs to real nos....f(0)=1 and f(x)is not equal to x..for any x belongs to real nos...then show that f(f(x)&gt;x for all positve real nos. thanks for help!

tushar a Grade: 11

        let f(x) be a continuous function for all x belongs to real nos....f(0)=1 and f(x)is not equal to x..for any x belongs to real nos...then show that f(f(x)>x for all positve real nos.

thanks for help!

8 years ago

Answers : (1)

Badiuddin askIITians.ismu Expert

147 Points

										Dear tshar
Case 1
f(x)>x   for all x ...................1
let x1 =f(x)
now   f(x1)>x1
put the value of x1
   f(f(x)) >f(x).................2
 from equation 1 and 2
or  f(f(x) >x  
Case 2
   f(x)<x   for all x
 put x=0
  f(x) <0
or  1<0   which is not possible 
so only first case is possible 


Please feel free to post as many doubts on our discussion forum as you can.
 If you find any question Difficult to understand - post it here and we will get you the answer and detailed solution very quickly.
 We are all IITians and here to help you in your IIT JEE  & AIEEE preparation. 
 All the best. 
 
Regards, 
Askiitians Experts 
Badiuddin