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2007 Moldova National Olympiad
11.4
Moldova NMO, 2007, XI Grade, Problem 4
Moldova NMO, 2007, XI Grade, Problem 4
Source: maybe this is Calculus..
March 3, 2007
function
algebra unsolved
algebra
Problem Statement
The function
f
:
R
→
R
f: \mathbb{R}\rightarrow\mathbb{R}
f
:
R
→
R
satisfies
f
(
cot
x
)
=
sin
2
x
+
cos
2
x
f(\textrm{cot}x)=\sin2x+\cos2x
f
(
cot
x
)
=
sin
2
x
+
cos
2
x
, for any
x
∈
(
0
,
π
)
x\in(0,\pi)
x
∈
(
0
,
π
)
. Find the minimum and maximum value of
g
:
[
−
1
;
1
]
→
R
g: [-1;1]\rightarrow\mathbb{R}
g
:
[
−
1
;
1
]
→
R
,
g
(
x
)
=
f
(
x
)
⋅
f
(
1
−
x
)
g(x)=f(x)\cdot f(1-x)
g
(
x
)
=
f
(
x
)
⋅
f
(
1
−
x
)
.
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