Let $f\left(x\right)=e^{\left\{e^{\left|x\right|}sgnx\right\}}$and $g\left(x\right)=e^{\left[e^{\left|x\right|} sgnx\right]} , x\in R$ where { } and [ ] denote the fractional and integral part functions, respectively. Also, $h\left(x\right)=\log \left(f\left(x\right)\right)+\log \left(g\left(x\right)\right).$ Then for real $x,h\left(x\right)$ is

• A

  an odd function

• B

  an even function

• C

  neither an odd nor an even function

• D

  both odd and even function