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Mathematics
Mathematics
Problem
Let
g
(
x
)
=
{
x
2
−
1
x
−
1
,
x
≠
1
,
2
,
x
=
1.
g(x)=\begin{cases}\dfrac{x^{2}-1}{x-1}, & x\neq1,\\ 2, & x=1.\end{cases}
g
(
x
)
=
⎩
⎨
⎧
x
−
1
x
2
−
1
,
2
,
x
=
1
,
x
=
1.
Is
g
(
x
)
g(x)
g
(
x
)
continuous at
x
=
1
x=1
x
=
1
? Give a brief reason for your answer.
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