If g:[-2, 2] to R where g(x) = x^3 + tan x + | vedclass

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(C) For $g(x)$ to be an odd function,it must satisfy $g(-x) = -g(x)$,which implies $g(x) + g(-x) = 0$.Given $g(x) = x^3 + 	an x + \left[ \frac{x^2 +

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$P > 5$

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(C) For $g(x)$ to be an odd function,it must satisfy $g(-x) = -g(x)$,which implies $g(x) + g(-x) = 0$.Given $g(x) = x^3 + 	an x + \left[ \frac{x^2 + 1}{P} ight]$.Then $g(-x) = (-x)^3 + 	an(-x) + \left[ \frac{(-x)^2 + 1}{P} ight] = -x^3 - 	an x + \left[ \frac{x^2 + 1}{P} ight]$.Adding these,$g(x) + g(-x) = 2 \left[ \frac{x^2 + 1}{P} ight] = 0$.This implies $\left[ \frac{x^2 + 1}{P} ight] = 0$ for all $x \in [-2, 2]$.For the greatest integer function to be zero,we must have $0 \le \frac{x^2 + 1}{P} Since $x \in [-2, 2]$,the maximum value of $x^2 + 1$ is $2^2 + 1 = 5$.Thus,we require $\frac{5}{P}  5$ (assuming $P > 0$ for the function to be well-defined in this context).

If $g:[-2, 2] \to R$ where $g(x) = x^3 + \tan x + \left[ \frac{x^2 + 1}{P} \right]$ is an odd function,then the value of the parameter $P$ is:

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