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

Answer: (A)

To check if the given function is

even or odd, replace $x$ by $-x$.

if $f\left(x\right)=f(-x)\Rightarrow$ even function.

if $f\left(x\right)=-f\left(x\right)\Rightarrow$ odd function.

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

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

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

$=f\left(x\right)$

Hence, $f\left(x\right)$ is even function

$\therefore \left(A\right)$ is the correct option.