Function $f(x)$ is defined as

$f(x)=\{\begin{array}{cc}2x-4,& x<mn>0</mn>\\ x^2& 3x-4,& x>0\\ 7,& x=0\end{array}$

Determine

$($a$)[5$ pts$]$ whether the limit $\underset{x0}{lim}f(x)$ exists, and

$($b$)[5$ pts$]$ whether the function is continuous at $x=0.$