# problem on continuity and differentiability

• Oct 18th 2010, 11:42 PM
Sambit
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

• Oct 19th 2010, 03:21 AM
mr fantastic
Quote:

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

This is the well-known Dirichlet function: Math Tutor - Functions - Theory - Elementary Functions
• Oct 19th 2010, 04:59 AM
Sambit
ya, but what about $f^2$?
• Oct 19th 2010, 09:58 AM
Also sprach Zarathustra
Modification 2.
• Oct 19th 2010, 12:29 PM
mr fantastic
Quote:

Originally Posted by Sambit
ya, but what about $f^2$?

I have provided you with a reference. You are now expected to think.
• Oct 19th 2010, 09:33 PM
Sambit
yes i understood.