Question

Function $f\left(x\right)={\log }_e(x^3+\sqrt{1+x^6})$ is

• A. even
• B. odd
• C. neither even nor odd
• D. none of these

Answer 1

The correct option is B odd

$f\left(x\right)=\log (x^3+\sqrt{1+x^6})$

$\therefore f(-x)=\log (-x^3+\sqrt{1+x^6})=\log [\frac{\sqrt{1+x^6}-x^3}{\sqrt{1+x^6}+x^3}.(\sqrt{1+x^6}+x^3\left)\right]$

$\Rightarrow f(-x)=\log \left[\frac{1+x^6-x^6}{\sqrt{1+x^6}+x^3}\right]=-\log (x^3+\sqrt{1+x^6})=-f\left(x\right)$

Hence $f\left(x\right)$ is an odd function.