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(A) The function $f(x) = [x]$ is known as the Greatest Integer Function. For any integer $n$,the left-hand limit is $\lim_{x 	o n^-} f(x) = n-1$ and

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continuous for all non-integral values of $x$

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(A) The function $f(x) = [x]$ is known as the Greatest Integer Function. For any integer $n$,the left-hand limit is $\lim_{x 	o n^-} f(x) = n-1$ and the right-hand limit is $\lim_{x 	o n^+} f(x) = n$. Since the left-hand limit is not equal to the right-hand limit at any integer $n$,the function is discontinuous at all integral values of $x$. However,for any non-integral value $c$ (where $c$ is not an integer),the function is locally constant in a small neighborhood around $c$,making it continuous at all such points. Therefore,the function $f(x) = [x]$ is continuous for all non-integral values of $x$.

The function $f(x) = [x]$,where $[x]$ denotes the greatest integer not greater than $x$,is

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