Question

Let $g:[-2,2]\to R$ ,where $g\left(x\right)=x^3+\tan x+\left[\frac{x^2+1}{p}\right]$ be an odd function, $[.]$ represent greatest integer function then the value of the parameter $p$ satisfies

• A. $\left|p\right|<5$
• B. $p<5$
• C. $p>5$
• D. None of these

Answer 1

Answer: (C)

$p>5$

For $g\left(x\right)$ to be odd function, $\left[\frac{x^2+1}{p}\right]$ has to be zero

given, $xϵ[-2,2]\Rightarrow x^2ϵ(0,4)\Rightarrow (x^2+1)ϵ[0,5]$

Hence for $\left[\frac{x^2+1}{p}\right]=0$, acceptable range of p is,

$p>5$
Hence, option 'C' is correct.