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India IMO Training Camp
2018 India IMO Training Camp
3
Functional Equation
Functional Equation
Source: India TST 2018 D1 P3
July 18, 2018
algebra
functional equation
Problem Statement
Find all functions
f
:
R
↦
R
f: \mathbb{R} \mapsto \mathbb{R}
f
:
R
↦
R
such that
f
(
x
)
f
(
y
f
(
x
)
−
1
)
=
x
2
f
(
y
)
−
f
(
x
)
,
f(x)f\left(yf(x)-1\right)=x^2f(y)-f(x),
f
(
x
)
f
(
y
f
(
x
)
−
1
)
=
x
2
f
(
y
)
−
f
(
x
)
,
for all
x
,
y
∈
R
x,y \in \mathbb{R}
x
,
y
∈
R
.
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