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2014 Iran Team Selection Test
4
easy function equation(question 4)
easy function equation(question 4)
Source: iran tst 2014 third exam
May 21, 2014
function
algebra proposed
algebra
functional equation
Problem Statement
Find all functions
f
:
R
+
→
R
+
f:\mathbb{R}^{+}\rightarrow \mathbb{R}^{+}
f
:
R
+
→
R
+
such that
x
,
y
∈
R
+
,
x,y\in \mathbb{R}^{+},
x
,
y
∈
R
+
,
f
(
y
f
(
x
+
1
)
)
+
f
(
x
+
1
x
f
(
y
)
)
=
f
(
y
)
f\left(\frac{y}{f(x+1)}\right)+f\left(\frac{x+1}{xf(y)}\right)=f(y)
f
(
f
(
x
+
1
)
y
)
+
f
(
x
f
(
y
)
x
+
1
)
=
f
(
y
)
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