Mathematics

Problem

The function

g

is defined by

g(x)=\begin{cases} \dfrac{1}{x^{2}-2x}, & x<1,\\ \sqrt{x+2}, & x\ge 1. \end{cases}

Which of the following statements about vertical asymptotes of

g

is correct? a)

g

has vertical asymptotes at

x=0

and

x=2

. b)

g

has a vertical asymptote only at

x=-2

. c)

g

has a vertical asymptote only at

x=0

. d)

g

has a vertical asymptote only at

x=1