Let f : R ->R be a function.

We say that f is Lipschitz continuous if there is some

L > 0 such that |f(x) − f(y)| < L|x − y| for all x, y in R.

lettingf, g : R -> Rbe lipschitz continious funtions,

(a) i want to show thatf+gis lipschitz continious too

and also iff,gare bounded lip continuos funtions

(b) then i want to show thatf.gis lipschitz continous too

does anyone know how to show these?