Question: How to limit a function to an interval

Hello,

I have a function, lets say g(x,y,...), that depends on many other functions. But I don´t want the results that are inside certain intervals, and I need to receive the results of those functions as something like NULL when asking for a result that is inside any of those intervals. That way, g(x,y,...) would also have to result in something like NULL if any of the lesser functions are NULL fora any given values.

I tryied using the piecewise command, and for the intervals that I wanted, it worked, but for those I wanted to be NULL, they were understood as 0, and so G(x,y,..) continued to exist but with a very different value.

To clarify what I need, I will try an exemple:

Imagine I have the function f(x)=x

I want to disconsider the results for x<2 and x>6, in a way that if I try the command 'f(1)', I will receive something like NULL and know that it is outside the range.

In the same way, I need the plot of this function f(X) to show the function only from 2 to 6, but not existing for the delimited intervals.

Ad if I continue and make g(x)=f(x)+10 , I don´t want g(x) to exist if f(x) doesn´t exist, and same for the g(x) plot, which shouldn´t be shown in the intervals where f(x) don´t exist.

Thank you very much for your atention!