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Pan-African Shortlist
2019 Pan-African Shortlist
A3
A3
Part of
2019 Pan-African Shortlist
Problems
(1)
Functional Equation: $f(x^2) - yf(y) = f(x + y)(f(x) - y)$.
Source: 2019 Pan-African Shortlist - A3
1/18/2021
Find all functions
f
:
R
→
R
f: \mathbb{R} \to \mathbb{R}
f
:
R
→
R
such that
f
(
x
2
)
−
y
f
(
y
)
=
f
(
x
+
y
)
(
f
(
x
)
−
y
)
f\left(x^2\right) - yf(y) = f(x + y) (f(x) - y)
f
(
x
2
)
−
y
f
(
y
)
=
f
(
x
+
y
)
(
f
(
x
)
−
y
)
for all real numbers
x
x
x
and
y
y
y
.
algebra
functional equation
function