Identity Function: How to Approach It?

[Gabbey]

Let's say I have a function that preservers ordering i.e if x<y then f(x)<f(y) for all x. Obviously it must follow that it's the identity function but how can I approach this?

 

[henry_m]

What about f(x)=2x? Think about what your condition means in terms of the graph of the function.

 

[Mark44]

Let's say I have a function that preservers ordering i.e if x<y then f(x)<f(y) for all x. Obviously it must follow that it's the identity function but how can I approach this?

It does not necessarily follow that f is the identify function. Any strictly increasing function satisfies the given conditions, not just f(x) = x.