Suppose that a function f is a subadditive prove that if f(0)=0 and if f is continuous at x=0 then f is continuous on all of R ?
how can i solve it ?
A function is continuous at a point if . Another characterization of continuity at (which is useful in your case) is that . ( of course is defined as
I would use the subadditivity of f along with the above characterization to show continuity at an arbitrary point.