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MathLinks Contest 3rd
1
0321 functional system 3rd edition Round 2 p1
0321 functional system 3rd edition Round 2 p1
Source:
May 9, 2021
algebra
3rd edition
Problem Statement
Find all functions
f
,
g
:
(
0
,
∞
)
→
(
0
,
∞
)
f, g : (0,\infty) \to (0,\infty)
f
,
g
:
(
0
,
∞
)
→
(
0
,
∞
)
such that for all
x
>
0
x > 0
x
>
0
we have the relations:
f
(
g
(
x
)
)
=
x
x
f
(
x
)
−
2
f(g(x)) = \frac{x}{xf(x) - 2}
f
(
g
(
x
))
=
x
f
(
x
)
−
2
x
and
g
(
f
(
x
)
)
=
x
x
g
(
x
)
−
2
g(f(x)) = \frac{x}{xg(x) - 2}
g
(
f
(
x
))
=
xg
(
x
)
−
2
x
.
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