Answer
Not continuous
Work Step by Step
We are given the function:
$f(x)=\dfrac{1}{x-3}$
We use the continuity checklist to determine if $f$ is continuous in $a=3$:
1) Determine the function's domain:
$x−3\not=0$
$x\not=3$
D=[2,∞)
a=1 is not in the function's domain, therefore f is not defined for a=1.
$D=(-\infty,3)\cup(3,\infty)$
As the condition 1 is not satisfied, the function is not continuous in $a=3$.
