Question

Given the equation f(x)=1/(x-2) -3, I can't find any critical values so is this a discontinuous equation?!

Answer 1

\[
f(x) = \frac{1}{(x-2)} - 3 \\
f'(x) = -\frac{1}{(x-2)^2} \\
\text{There is no solution to }f'(x) = 0.\\
f'(x) \text { is undefined at x = 2.} \\
\text{However, x = 2 is NOT a critical point because f(x) does not exist at x = 2 either.}\\
\text{No critical points for this function.}
\]