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Mathematics
Problem
Let
g
g
g
be a continuous, strictly decreasing function on
[
−
3
,
5
]
[-3,5]
[
−
3
,
5
]
with
g
(
−
3
)
=
7
g(-3)=7
g
(
−
3
)
=
7
and
g
(
5
)
=
2
g(5)=2
g
(
5
)
=
2
. Explain why
g
−
1
g^{-1}
g
−
1
is continuous on
[
2
,
7
]
[2,7]
[
2
,
7
]
.
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