I need an algorithm which has the following property:
$f(x)$ will lie between $[a, b]$ (both integers) when $x$ is an element of $[a, b]$
There should be no collisions i.e. $f(x)$ should always be unique for unique $x$
The simplest function is $f(x) = x$. Can there be a family of such functions? How can I mathematically represent it?
In simple words - I want a function which can distribute all numbers between $[a,b]$ in the output set which is also $[a,b]$.
Sorry I am not a mathematician :) So this is the best I can do to express what I need :)