Can Two Discontinuous Functions Sum to a Continuous Function?

[phrances]

can you give me an example of two discontinuous functions at a number a whose sum is not discontinuous at a? thanks!:shy:

 

[feod2003]

i was just about to ask a question about dis. functions, and express each function as a composition, and i don't know how to do that??

if you give me a prob, i might help to see what you mean.

 

[interested_learner]

huh?

If the functions are discontinuous at a, then their sums are not going to be continuous at a. I suppose you could have two step functions, one going up and one going down, but I don't think that is really fair because there is still a discontinunity at a... Mathematicians?

 

[arildno]

Let f(x)=0 when x is not zero, and 1 when x is zero.
Let g(x)=0 when x is not zero, and -1 when x is zero.

then f+g is continuous everywhere.