The function $f:(-\infty ,\infty )\to (-\infty ,\infty )$ defined by $f\left(x\right)=e^{\left|x\right|}$ is

The correct option is B neither one - one nor onto
$f:(-\infty ,\infty )\to (-\infty ,\infty )$ for $f\left(x\right)=e^{|x|})$
as $f(-1)=f\left(1\right)=e$ hence $f$ is not one-one.
as $f\left(x\right)=e^{|x|}>0\forall xϵR$
thus range of $f\ne$ codomain $\Rightarrow f$ is not onto.