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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!

7 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





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Badiuddin

7 years ago
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