Q: Let f:[0,1]->[0,1] be a function defined as follows.

Take x in [0,1] with the decimal expansion x=.x1x2x3x4x5.....

Map it to y in [0,1] such that y=.x1x3x5......

Prove that this map is continuous but nowhere differentiable in [0,1].

I need some help for this problem.

If anybody has a solution please mail me at ppcparichoy@gmail.com