# Thread: problem on continuity and differentiability

1. ## problem on continuity and differentiability

Let, f(x) = x , if x is rational
= 0 , if x is irrational.

Then at x=0, which one of he followings is true?
(a) both f and $f^2$ are differentiable
(b) neither f nor $f^2$ are differentiable
(c) $f^2$ is continuous but not differentiable
(d) $f^2$ is differentiable but f is not

please help.

2. Originally Posted by Sambit
Let, f(x) = x , if x is rational
= 0 , if x is irrational.

Then at x=0, which one of he followings is true?
(a) both f and $f^2$ are differentiable
(b) neither f nor $f^2$ are differentiable
(c) $f^2$ is continuous but not differentiable
(d) $f^2$ is differentiable but f is not

please help.
This is the well-known Dirichlet function: Math Tutor - Functions - Theory - Elementary Functions

3. ya, but what about $f^2$?

4. Modification 2.

5. Originally Posted by Sambit
ya, but what about $f^2$?
I have provided you with a reference. You are now expected to think.

6. yes i understood.