JEE Main & Advanced Mathematics Functions Discontinuous Function

Discontinuous Function

Category : JEE Main & Advanced

(1) Discontinuous function : A function \['f'\] which is not continuous at a point \[x=a\] in its domain is said to be discontinuous there at. The point \['a'\] is called a point of discontinuity of the function.



The discontinuity may arise due to any of the following situations.



(i) \[\underset{x\to {{a}^{+}}}{\mathop{\lim }}\,f(x)\] or \[\underset{x\to {{a}^{-}}}{\mathop{\lim }}\,f(x)\] or both may not exist



(ii) \[\underset{x\to {{a}^{+}}}{\mathop{\lim }}\,f(x)\]as well as \[\underset{x\to {{a}^{-}}}{\mathop{\lim }}\,f(x)\] may exist, but are unequal.



(iii)\[\underset{x\to {{a}^{+}}}{\mathop{\lim }}\,f(x)\] as well as \[\underset{x\to {{a}^{-}}}{\mathop{\lim }}\,f(x)\] both may exist, but either of the two or both may not be equal to \[f(a)\].

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