Question

Among the following which is odd function

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

(a) $f\left(x\right)=\frac{a^x+a^{-x}}{2}$ and f (– x) = f(x)
(b) $f\left(x\right)=\frac{x}{e^x-1}+\frac{x}{2}$ and f(x) – f (–x) = 0
(c) $f\left(x\right)=\sqrt{1+x+x^2}+\sqrt{1-x+x^2}$
$\Rightarrow$ f(–x) = f(x) $\Rightarrow$ ‘f’ is even
(d) $f\left(x\right)=x^3+sinx$ f(–x) = –f(x) $\Rightarrow$ ‘f’ is odd.