If ;$\displaystyle f(x)=sgn(x^{5})$ then which of the following is/are false (where sgn denotes signum function)

$\displaystyle f\left ( x \right )=sgn\left ( x^{5} \right )=1$ if $x > 0$

$\displaystyle f\left ( x \right )=sgn\left ( x^{5} \right )=0$ if $x = 0$

$\displaystyle f\left ( x \right )=sgn\left ( x^{5} \right )=-1$ if $x < 0$

$\displaystyle f'\left ( 0^{+} \right )=\lim_{h\rightarrow 0}\frac{1-0}{h}=DNE$

$\displaystyle f'\left ( 0^{-} \right )=\lim_{h\rightarrow 0}\frac{-1-0}{-h}=DNE$

Also, $\displaystyle f\left ( 0^{+} \right )=1\: \: \&\: \: f\left ( 0^{-} \right )=-1$

$\displaystyle \Rightarrow$ $f$ is neither continuous not differentiable at $x = 0$