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Mathematics
Problem
A function
f
f
f
is continuous everywhere except that
f
(
3
)
f(3)
f
(
3
)
is undefined and
lim
x
→
3
f
(
x
)
=
2
\displaystyle \lim_{x\to 3}f(x)=2
x
→
3
lim
f
(
x
)
=
2
. Define
g
(
x
)
=
∣
f
(
x
)
∣
g(x)=|f(x)|
g
(
x
)
=
∣
f
(
x
)
∣
for all
x
x
x
where
f
(
x
)
f(x)
f
(
x
)
is defined. Determine whether
g
g
g
is continuous at
x
=
3
x=3
x
=
3
and state the type of any discontinuity there.
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