can a discontineous function be differentiable under some transformation ?

Answer 1

Good question. What kind of transformations are you talking about ? If any transformation, the original function is transformed to a contineous function, then it may be differentiable. Remember a discontineous function is never differentiable, and a contineous function is not always differentiable. It really depends on what type of transformation you perform.

Hope this was helfpul.

Answer 2

you should specify what kind of transformations are allowed , an homeomorphism definitaly not.,

also there are different kind of definitions of differentiable