Define the function f(x)= cases x^ 2 -1 x-1 , & x<1, 4, & x=1, 3-x, & 1<x<2, (x-2), & x 2

MATHEMATICS · Subjective · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Define the function

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

List every point at which

f

is discontinuous and, for each point, state whether the discontinuity is removable, jump, or infinite.