Question

If $f\left(x\right)$ is an odd function, then $|f\left(x\right)|$ is

• A. an odd function
• B. an even function
• C. neither odd nor even
• D. even and odd

Answer 1

The correct option is B an even function

If $f\left(x\right)$ is an odd function,

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

Let $g\left(x\right)=|f\left(x\right)|$

$\Rightarrow$ $g(-x)=|f(-x)|$

$\Rightarrow$ $g(-x)=|-f\left(x\right)|$

$\Rightarrow$ $g(-x)=|-1||f\left(x\right)|$

$\Rightarrow$ $g(-x)=|f\left(x\right)|=g\left(x\right)$

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