2 functions f,g:X -> X that are discontinuous

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2 functions f,g:X --> X that are discontinuous

looking for 2 functions f,g:X --> X that are discontinuous but their composition gof continuous...
 

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matt grime
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Assuming X=R, the reals, can you think of someway of using the fuction that is 0 if x=0, and 1 otherwise with a similar function?
 

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