For the first one, one example is with being the delta function defined as
I'm not quite understanding what you're asking for in your second problem. A piecewise function that satisfies the limits provided is
Hopefully that's what you meant.
I wanted to find an example for a function that maintains the following conditions:
1. f(x)=? if all the following conditions are correct.
2. if all the following conditions are correct: f(x) is a function that defined in a split domain. I need to find examples for f(x);x>=0 and for f(x);x<0.