Question

If $f\left(x\right)=\sqrt[n]{n{x}^m}$ is an even function, then $m$ is

• A. an even integer
• B. an odd integer
• C. any positive integer
• D. any real number

Answer 1

The correct option is A an even integer

Clearly $n\in N>1$
Since $f\left(x\right)$ is an even function
$\Rightarrow f\left(x\right)=f(-x)\Rightarrow \sqrt[n]{n{x}^m}=\sqrt[n]{n(-x{)}^m}\Rightarrow x^m=(-x{)}^m\Rightarrow m=2k,\text{where}k\in I$
So, $m$ is an even integer