1. ## Continuous Function

Give examples of some functions which are continuous at only one point and discontinuous at all other points of the interval.[B]THANKS

2. Originally Posted by kamranqau
Give examples of some functions which are continuous at only one point and discontinuous at all other points of the interval.[B]THANKS
The classic example is the function

$f(x) = \left\{ \begin{array}{cl}x, & \mbox{ if } x \mbox{ is rational}\\-x, & \mbox{ if } x \mbox{ is irrational}\end{array}\right.$

It is continuous only at x = 0.