Question

If $f\left(x\right)=\sqrt[3]{3(1-x^2)}+\sqrt[3]{3(1+x^2)},$ then $f\left(x\right)$ is

• A. an even function
• B. an odd function
• C. constant function
• D. None of these

Answer 1

The correct option is A an even function

$f\left(x\right)=\sqrt[3]{3(1-x^2)}+\sqrt[3]{3(1+x^2)}$

$f(-x)=\sqrt[3]{3(1-(-x{)}^2)}+\sqrt[3]{3(1+(-x{)}^2)}$

$f(-x)=\sqrt[3]{3(1-x^2)}+\sqrt[3]{3(1+x^2)}=f\left(x\right)$

$\because f\left(x\right)=f(-x)$

$\therefore f\left(x\right)$ is an even function

Answer: option (A)