Determine the interval$($s$)$ on which the function $f(x)=e^{\sqrt[\phantom{2}]{x-2}}$ is continuous, then evaluate the limits $\underset{x6}{lim}f(x)$ and $\underset{x{2}^{}}{lim}f(x)$

Choose the correct answer below.

A$.[2,)$ B$.(-,)$

C$.(-\mathrm{.}2)$ D$.(2)$

$\underset{x6}{lim}f(x)=$

$($Type your answer using exponential notation.$)$

en and $$

$x-2^{}$