I"m trying to think of 2 functions that are discontinuous at point C, but when added togther, and multiplied togther, will be continuous at point c. I tried 1/x, root(x), a polynomail w/ x-1 in the denomiator....cant think of anything....any hints? I mean, when you multiply 2 functions to get a new function, can't you factor that function back to the original function, and it will be discontinuous again?
Think quite a bit simpler. Hint: Try two functions that are "almost constant," ie. they are constant except at [itex]C[/itex] where they are both discontinuous. Don't forget that defining functions piecewise is perfectly allowable.