f(x)=1-mod(x) when mod(x)<=1 and 0 when mod(x)>1
g(x)=f(x-1)+f(x+1) for every x belonging to real no
discuss continuity and differentiation
You have shown no effort here (and that includes the fact that you posted this question in the Pre-calculus subforum with the title Calculus).
If you want help, show some effort. What have you tried? Where are you stuck? (At the very least, make an effort to post in the correct subforum using a descriptive title).