Discontinuity of a Function

by Babukutty Daniel
(New York)

Can you give me an example of a function f(x) such that its limit as x approaches a from right and that as x approaches a from left are equal, the function is defined at the point a but the function is not continuous at the point a?




Answer by Pablo:

Your question is interesting. And the best answer is just a graph:



In this function both lateral limits equal 2 at point a, but they don't equal the value of f(a). So, it isn't continuous. For more details about how to determine whether a function is continuous or not: Continuous Functions: An Intuitive Introduction.

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