Bound function result - mathematical formulation excuse me for the quite simple question. 
Let us assume that we have the function $f(x)=\frac{a-x}{a}$ where $x \in  \mathbb{R} $ and $a$ is a scalar.
I want to mathematically express that the outcome of the function should belong to the set $[0,\infty) $, thus if the outcome is negative is should be changed to zero.
How should the formula be writen?

If you are allowed to change the definition of $f$, then simply take
$$f(x)=\begin{cases} 
      {a-x\over a} & x\leq a \\
      0 & otherwise 
   \end{cases}
.$$
Now "the outcome" (the image) of $f$ is defined over $[0,\infty)$.
Edit: Note that the number $a$ can only be an scalar different than $0$ for the function to be well-defined. 
