For a real number \( y \), let \( [y] \) denote the greatest intege...

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For a real number \( y \), let \( [y] \) denote the greatest integer less than or equal to \( y \). Then
\[
f(x)=\frac{\tan (\pi[x-\pi])}{1+[x]^{2}}
\]
is
(a) discontinuous at some \( x \)
(b) continuous at all \( x \), but the derivative \( f^{\prime}(x) \) does not exist for some \( x \)
(c) \( f^{\prime}(x) \) exists for al1 \( x \) but the second derivative
\( f^{\prime \prime}(x) \) does not exist
(d) \( f^{\prime}(x) \) exists for all \( x \)
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