If `g:[-2,2]vecR` , where `f(x)=x^3+tanx+[(x^2+1)/P]` is an odd function, then the value of parametric P, where [.] denotes the greatest integer function, is

Options

A. `-5 lt P lt 5`
B. `P lt 5`
C. `P gt 5`
D. None of these

Answer

C

Explanation

`g(x)=x^(3)+tanx+[(x^(2)+1)/(P)]`
`or g(-x)=(-x)^(3)+tan(-x)+[((-x)^(2)+1)/(P)]`
`= -x^(3)-tanx+[(x^(2)+1)/(P)]`
Since g(x) is odd,
`g(x)+g(-x)=0`
` :. (-x^(3)-tanx+[(x^(2)+1)/(P)])+((-x^(3)-tanx),(+[(x^(2)+1)/(P)]))=0`
` or 2[((x^(2)+1))/(P)]=0 or 0 le (x^(2)+1)/(P) lt 1`
Now, ` x in [-2, 2]`
` :. x^(2)+1 in [1,5]`
` :. P gt 5`