Odd and Even Functions

Let $f\left(x\right)=e^{\left\{e^{\left|x\right|}\mathit{sgn}x\right\}}$ and $g\left(x\right)=e^{\left[e^{\left|x\right|}\mathit{sgn}x\right]}, x\in R$, where $\left\{.\right\}$ and $\left[.\right]$ 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

If the graph of the function $f\left(x\right)=\frac{a^x-1}{x^n\left(a^x+1\right)}$ is symmetrical about $y$-axis, then $n$ equals

Let $f\left(x\right)=\left({\left[a\right]}^2-5\left[a\right]+4\right)x^3-\left(6{\left\{a\right\}}^2-5\left\{a\right\}+1\right)x-\left(\tan x\right)\times sgnx$ be an even function for all $x\in R,$ then the
sum of all possible values of $\text{'}a\text{'}$ is (where $\left[.\right]$ and $\left\{.\right\}$ denote the greatest integer function and fractional part functions, respectively)

$f\left(x\right)=\frac{\cos x}{\left[\frac{2x}{\pi }\right]+\frac{1}{2}},$ where $x$ is not an integral multiple of $\pi$ and $\left[.\right]$ denotes the greatest integer function is

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