$$f(x)=[arctan(x)] $$ we are given this problem to check this function's continuity and find out where it's discontinuous , note that $$ donotes greatest integer function now the problem comes when we have to get that value of $arctan(x)$ which is $\ge 1$ and $\le -1$ now how do we go on to find out this?
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Hint: Greatest integer function is discontinuous at integer points. Therefore, the given function will be discontinuous when arctan(x) is an integer.