### Proof Regarding Continuous Functions

Let f be a function defined on all of R that satisfies the additive condition f(x+y)=f(x)+f(y) for all x,y belong to R a- Show that f(0)=0 and that f(-x)=-f(x) for all x belong to R. b- Show that if f is continuous at x=0 then f is continuous at every point in R c- Let k=f(1) show that f f(n)=kn for all n belong to N and