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$If g : [- 2, 2] \to R, where f (x) = x^{3} + \tan x + [\frac{x^{2} + 1}{P}] is an odd function, then the value of parametric P, where [.]$ $d e n o t e s t h e g r e a t e s t i n t e g e r f u n c t i o n, i s$

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−5

P<5

P>5

None of these

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detailed solution

Correct option is C

g(x)=x3+tan⁡x+x2+1P or g(−x)=(−x)3+tan⁡(−x)+(−x)2+1P =−x3−tan⁡x+x2+1P Now, g(x)+g(−x)=0 Because g(x) is a odd function, x3+tan⁡x+x2+1P+−x3−tan⁡x+x2+1P=0 or 2x2+1P=0 or 0≤x2+1P<1 Now, x∈[−2,2]∴ 0≤5P<1 or P>5

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If g:[−2,2]→R, where f(x)=x3+tan⁡x+x2+1P is an odd function, then the value of parametric P, where [.]denotes the greatest integer function, is

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$If g : [- 2, 2] \to R, where f (x) = x^{3} + \tan x + [\frac{x^{2} + 1}{P}] is an odd function, then the value of parametric P, where [.]$ $d e n o t e s t h e g r e a t e s t i n t e g e r f u n c t i o n, i s$