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If $g:[-2,2] \rightarrow R$ where $g(x)=x^3+\tan x+\left[\frac{x^2+1}{P}\right]$ is a odd function then the value of parametric $P$ is
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$P\gt5$
$\begin{aligned} & g(x)=x^3+\tan x+\frac{x^2+1}{P} \\ & g(-x)=(-x)^3+\tan (-x)+\frac{(-x)^2+1}{P} \\ & g(-x)=-x^3-\tan x+\frac{x^2+1}{P} \\ & g(x)+g(-x)=0 \text { because } g(x) \text { is a odd function } \\ & \therefore\left[x^3+\tan x+\frac{x^2+1}{P}\right]+\left[-x^3-\tan x+\frac{x^2+1}{P}\right]=0 \\ & \Rightarrow \frac{2\left(x^2+1\right)}{P}=0 \Rightarrow 0 \leq \frac{x^2+1}{P} \lt 1 \text { because } x \in[-2,2] \\ & \Rightarrow 0 \leq \frac{5}{P} \lt 1 \Rightarrow P\gt5 .\end{aligned}$
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