Mathematics

Mathematics

Problem

Consider the function

g(x)= \begin{cases} \dfrac{|x-1|}{\,x-1\,}, & x\neq1,\\ 0, & x=1. \end{cases}

At which of the following point(s), if any, is

g

not continuous? a) At

x=1

and

x=0

b) Only at

x=1

c) At every real

x

d) At no point (continuous everywhere)

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