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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!

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!

Grade:11

1 Answers

Badiuddin askIITians.ismu Expert
147 Points
11 years ago

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


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Badiuddin

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