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If $g : [- 2, 2] \to R$ where $f (x) = x^{3} + \tan x + [\frac{x^{2} + 1}{P}]$ is a odd function then the value of paramer ‘P’ is, where [.] denotes the greatest integer function

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$- 5 < P < 5$

$P = 5$

$P > 5$

$P < 5$

answer is C.

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Detailed Solution

$g (x) + g (- x) = 0$
Because g(x) is a odd function
$\Rightarrow 2 [\frac{(x^{2} + 1)}{P}] = 0 \Rightarrow 0 \leq \frac{x^{2} + 1}{P} < 1 \Rightarrow P > 5 as x \in [- 2, 2]$

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