Mathematics

Problem

The function

g

is given by

g(x)= \begin{cases} \dfrac{x+1}{x-4}, & x<4,\\ \sqrt{x-3}, & x\ge 4. \end{cases}

Determine

\lim_{x\to 4^-} g(x)

and state whether

x=4

is a vertical asymptote of

g