a function.... (1 Viewer)

[roadrage75]

The function f has domain R and it is continuous at the point 0.

It satifisfies the condition: f(x+y) = f(x) + f(y). Prove f is contintinuous at point a, for all real a.

im lost as to what to do! i've worked out, and i think im right, that f(0) must = 0, but apart from that i'm stuck.

I have tried implicitly differentiating both sides, which did get me an answer, but somehow, i don't think i'm supposed to do it that way. Any ideas?

 

[Affinity]

then you go

lim [h-> 0] |f(a+h)-f(h)| = lim [h -> 0] |f(h)| = 0

so f is continuous at a. or even without hte absolute value signs