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2
Functional Equation
Functional Equation
Source: India TST 2016 Day 4 Problem 2
July 22, 2016
functional equation
function
algebra
Problem Statement
Find all functions
f
:
R
→
R
f:\mathbb{R}\to\mathbb{R}
f
:
R
→
R
such that
f
(
x
3
+
f
(
y
)
)
=
x
2
f
(
x
)
+
y
,
f\left(x^3+f(y)\right)=x^2f(x)+y,
f
(
x
3
+
f
(
y
)
)
=
x
2
f
(
x
)
+
y
,
for all
x
,
y
∈
R
.
x,y\in\mathbb{R}.
x
,
y
∈
R
.
(Here
R
\mathbb{R}
R
denotes the set of all real numbers.)
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