Thank you for responding. Actually I need a function which should be monotonically increasing and converts any +ve number to a number within the range 0 to 1. (The function should use the whole range between 0 to 1. For example for 1/(1+x) as the value of x increase, the function gives less value, I want the opposite).
Then . That is an increasing function and maps into .
If, by "The function should use the whole range between 0 and 1." you mean that the function should have both the values 0 and 1, as well as all values between, for some finite, x, that is impossible for an increasing function on .