Discontinuous composite of continuous functions

[M Dhanota]

Homework Statement

give an example of functions f and g, both continuous at x=0, for which the composite f(g(x)) is discontinuous at x=0. Does this contradict the sandwich theorem? Give reasons for your answer.

Homework Equations

The Attempt at a Solution

I understand the sandwich theorem, but I don't understand how I can just make up these functions!

 

[Office_Shredder]

If f(g(x)) is discontinuous, what can we say about f(x) or g(x)?

 

[M Dhanota]

I really want to say that one of the functions, either f(x) or G(x) is also discontinuous at a certain point. But not at x=0.