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Mathematics
Problem
Let
g
g
g
be defined by
g
(
x
)
=
∣
x
−
2
∣
g(x)=|x-2|
g
(
x
)
=
∣
x
−
2∣
for
x
≠
1
x\ne 1
x
=
1
, and
g
g
g
is not defined at
x
=
1
x=1
x
=
1
. Determine whether
g
′
(
1
)
g'(1)
g
′
(
1
)
exists and state the reason for your conclusion.
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