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Postal Coaching
2008 Postal Coaching
4
f(xf(y))= (1 - y)f(xy) + x^2y^2f(y)
f(xf(y))= (1 - y)f(xy) + x^2y^2f(y)
Source: Indian Postal Coaching 2008 set 2 p4
May 25, 2020
functional
functional equation
algebra
Problem Statement
Find all functions
f
:
R
→
R
f : R \to R
f
:
R
→
R
such that
f
(
x
f
(
y
)
)
=
(
1
−
y
)
f
(
x
y
)
+
x
2
y
2
f
(
y
)
f(xf(y))= (1 - y)f(xy) + x^2y^2f(y)
f
(
x
f
(
y
))
=
(
1
−
y
)
f
(
x
y
)
+
x
2
y
2
f
(
y
)
for all reals
x
,
y
x, y
x
,
y
.
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