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2011 Kosovo National Mathematical Olympiad
2
KMO #2 (Grade 11) [Transformation Problem]
KMO #2 (Grade 11) [Transformation Problem]
Source:
March 13, 2011
function
quadratics
algebra proposed
algebra
Problem Statement
Is it possible that by using the following transformations:
f
(
x
)
↦
x
2
⋅
f
(
1
x
+
1
)
or
f
(
x
)
↦
(
x
−
1
)
2
⋅
f
(
1
x
−
1
)
f(x) \mapsto x^2 \cdot f \left(\frac{1}{x}+1 \right) \ \ \ \text{or} \ \ \ f(x) \mapsto (x-1)^2 \cdot f\left(\frac{1}{x-1} \right)
f
(
x
)
↦
x
2
⋅
f
(
x
1
+
1
)
or
f
(
x
)
↦
(
x
−
1
)
2
⋅
f
(
x
−
1
1
)
the function
f
(
x
)
=
x
2
+
5
x
+
4
f(x)=x^2+5x+4
f
(
x
)
=
x
2
+
5
x
+
4
is sent to the function
g
(
x
)
=
x
2
+
10
x
+
8
g(x)=x^2+10x+8
g
(
x
)
=
x
2
+
10
x
+
8
?
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