Let, \( f(x)=\left[\begin{array}{ll}\frac{8}{\pi} \tan ^{-1}(-|x|+3...

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Let, \( f(x)=\left[\begin{array}{ll}\frac{8}{\pi} \tan ^{-1}(-|x|+3), & |x|2 \\ {\left[\frac{3 x^{2}-|x|+3}{x^{2}+1}\right],} & |x| \leq 2\end{array}\right. \)
\( \mathrm{P} \)
Number of integers in the range of \( f(x) \) is where [] denotes greatest integer function.
(a) 5
(b) 6
(c) 7
(d) more than 7
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