Comments by chorgeshashank1729
How did you assume it is differentiable. I saw your other answers as well where you assumed the property of being differential and fortunately the functions were nice. But your solution is not complete. I can assume the function is injective and get the answer right away.
I found the answer and it is little more complicated but makes assumption that the fixed point is an integer greater than 1. I am trying to fix this but seems difficult
Your answer is wrong. You never made use of the fact that fixed point is greater than 1. You just used the fact it is positive which is not sufficient. Take f(x)= 2x^2 fixed point is 1/2 and satisfies both conditions but it is not identity map.