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Pan African
2012 Pan African
2
Find all functions from reals to reals
Find all functions from reals to reals
Source: Pan African MO 2012 Day 2 Q2
October 14, 2012
function
algebra proposed
algebra
Problem Statement
Find all functions
f
:
R
→
R
f:\mathbb{R}\rightarrow\mathbb{R}
f
:
R
→
R
such that
f
(
x
2
−
y
2
)
=
(
x
+
y
)
(
f
(
x
)
−
f
(
y
)
)
f(x^2 - y^2) = (x+y)(f(x) - f(y))
f
(
x
2
−
y
2
)
=
(
x
+
y
)
(
f
(
x
)
−
f
(
y
))
for all real numbers
x
x
x
and
y
y
y
.
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