Question

If $g:[2:2]\to R$ where $g\left(x\right)=x^3+tanx+\left[\frac{x^2+1}{p}\right]$ is a odd function then the value of parametric P is

• A. -5<P<5
• B. P<5
• C. P>5
• D. None of these

Answer 1

The correct option is C P>5

$g\left(x\right)=x^3+tanx+\frac{x^2+1}{p}$

$g(-x)=(-x{)}^3+tan(-x)+\frac{(-x{)}^2+1}{p}$

$g(-x)=-x^3-tanx+\frac{x^2+1}{p}$

$g\left(x\right)+g(-x)=0$ because g(x) is a odd function

$\therefore [x^3+tanx+\frac{x^2+1}{p}]+[-x^3-tanx+\frac{x^2+1}{p}]=0$

$\Rightarrow \frac{2(x^2+1)}{p}=0$

$\Rightarrow 0\le \frac{x^2+1}{p}<1$ because $x\in [-2,2]$

$\Rightarrow 0\le \frac{5}{p}<1\Rightarrow p>5.$