Continuety of sum of functions

[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?

prove and give exmple to support your answer

??

 

[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.

 

[NoMoreExams]

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

 

[transgalactic]

i don't know how to prove such things
??

 

[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