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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!

8 years ago

## Answers : (1)

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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8 years ago
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