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2023-IMOC
A2
Reals to reals FE
Reals to reals FE
Source: IMOC 2023 A2
September 9, 2023
algebra
Problem Statement
Find all functions
f
:
R
→
R
f:\mathbb{R} \rightarrow \mathbb{R}
f
:
R
→
R
, such that
f
(
f
(
x
)
+
y
)
(
x
−
f
(
y
)
)
=
f
(
x
)
2
−
f
(
y
2
)
.
f(f(x)+y)(x-f(y)) = f(x)^2-f(y^2).
f
(
f
(
x
)
+
y
)
(
x
−
f
(
y
))
=
f
(
x
)
2
−
f
(
y
2
)
.
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