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2018 Nepal National Olympiad
2c
2c
Part of
2018 Nepal National Olympiad
Problems
(1)
Nepal National Olympiad
Source: Nepal Mathematics Olympiad
4/22/2018
Problem Section #2c). Denote by
Q
+
\mathbb{Q^+}
Q
+
the set of all positive rational numbers. Determine all functions
f
:
Q
+
→
Q
+
f:\mathbb{Q^+}\to\mathbb{Q^+}
f
:
Q
+
→
Q
+
which satisfy the following equation for all
x
,
y
∈
Q
+
:
f
(
f
(
x
)
2
.
y
)
=
x
3
.
f
(
x
y
)
x,y \in \mathbb{Q^+} : f(f(x)^2.y)=x^3.f(xy)
x
,
y
∈
Q
+
:
f
(
f
(
x
)
2
.
y
)
=
x
3
.
f
(
x
y
)
.
functions
algebra