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8
f(x)f(yf(x)-1)=x^2f(y)-f(x)
f(x)f(yf(x)-1)=x^2f(y)-f(x)
Source: Ukraine TST 2015 p8
May 2, 2020
functional equation
functional
algebra
Problem Statement
Find all functions
f
:
R
→
R
f: R \to R
f
:
R
→
R
such that
f
(
x
)
f
(
y
f
(
x
)
−
1
)
=
x
2
f
(
y
)
−
f
(
x
)
f(x)f(yf(x)-1)=x^2f(y)-f(x)
f
(
x
)
f
(
y
f
(
x
)
−
1
)
=
x
2
f
(
y
)
−
f
(
x
)
for all real
x
,
y
x ,y
x
,
y
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