Find the domain of the function and justify your answer with algebraic work.

$f(x)=\frac{2}{x1}\sqrt[3]{x-1}\sqrt[\phantom{2}]{x5}$

Find the limit$,\underset{x4}{lim}g(x),$ If it exists, otherwise explain why it does not exist. $g(x)=\{\begin{array}{cc}\sqrt[\phantom{2}]{8x-32},& x4\\ 0\mathrm{.}5x^2-8,& x<mn>4</mn>\end{array}$