Mathematics

Problem

A function

f

is defined by

f(x)= \begin{cases} \dfrac{x^{2}-1}{x-1}, & x<1,\\ \sqrt{2x-2}, & 1\le x\le4,\\ \ln(x-3), & x>4. \end{cases}

Which of the following correctly describes the set of all points where

f

is continuous? a)

(-\infty,1]\cup(1,4]\cup(4,\infty)

(-\infty,1)\cup(1,3)\cup(3,4)\cup(4,\infty)

(-\infty,1)\cup(1,4)\cup(4,\infty)

(-\infty,1)\cup(1,4]\cup(4,\infty)