Continuety of sum of functions

1. Dec 29, 2008

transgalactic

A.does f(x) +g(x) continues in X0 when
f(x) continues in X0 but g(x) doesnt?

B.does f(x) +g(x) continues in X0 when both
f(x) and g(x) are not continues in X0?

??

2. Dec 29, 2008

jgens

If you're uncertain whether or not each function is continuous, try to constuct a counter example satisying the initial premises. After that, prove whatever result you obtained.

3. Dec 29, 2008

NoMoreExams

For b) consider functions that have discont. but for example sum to be some constant.

Last edited: Dec 29, 2008
4. Dec 29, 2008

transgalactic

i dont know how to prove such things
??

5. Dec 29, 2008

NoMoreExams

Are you sure you are supposed to prove them? b) is false using the example I gave so come up with a counterexample using the logic that I told you