# 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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