Find the range of `f(x)=(x-[x])/(1-[x]+x '),w h e r e[]` represents the greatest integer function.

Explanation

`f(x)=(x-[x])/(1-[x]+x)=({x})/(1+{x})=1-(1)/(1+{x})`
Now, `0 le {x} lt1`
or `1 le {x} +1 lt 2`
or `(1)/(2) lt (1)/(1+{x}) le 1`
or `-1 le -(1)/(1+{x}) lt -(1)/(2)`
or ` 0 le 1-(1)/(1+{x}) lt (1)/(2)`