Question

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

Since $f\left(x\right)$ is odd, we have

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

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

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

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

Hence, option B is correct.