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Mathematics
Mathematics
Problem
Let
f
:
R
→
R
f: \mathbb{R} \to \mathbb{R}
f
:
R
→
R
and
f
(
x
)
=
3
x
2
+
m
x
+
n
x
2
+
1
f(x) = \frac{3x^2 + mx + n}{x^2 + 1}
f
(
x
)
=
x
2
+
1
3
x
2
+
m
x
+
n
. If the range of this function is
[
−
4
,
3
]
[-4, 3]
[
−
4
,
3
]
, then the value of
m
2
+
n
2
4
\frac{m^2 + n^2}{4}
4
m
2
+
n
2
is .....
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