A function is defined by f(x)= cases x^ 2 -1 x-1 , & x4

MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity

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)

(b)

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

(c)

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

(d)

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