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India IMO Training Camp
2001 India IMO Training Camp
2
Functional equation !
Functional equation !
Source: India TST 2001 Day 3 Problem 2
January 31, 2015
function
algebra
polynomial
algebra proposed
Problem Statement
Find all functions
f
:
R
+
→
R
+
f \colon \mathbb{R_{+}}\to \mathbb{R_{+}}
f
:
R
+
→
R
+
satisfying :
f
(
f
(
x
)
−
x
)
=
2
x
f ( f (x)-x) = 2x
f
(
f
(
x
)
−
x
)
=
2
x
for all
x
>
0
x > 0
x
>
0
.
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