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Turkey Team Selection Test
2017 Turkey Team Selection Test
7
7
Part of
2017 Turkey Team Selection Test
Problems
(1)
Turkey TST Functional Equality
Source: Turkey Team Selection Test 2017 P7
4/6/2017
Let
a
a
a
be a real number. Find the number of functions
f
:
R
→
R
f:\mathbb{R}\rightarrow \mathbb{R}
f
:
R
→
R
depending on
a
a
a
, such that
f
(
x
y
+
f
(
y
)
)
=
f
(
x
)
y
+
a
f(xy+f(y))=f(x)y+a
f
(
x
y
+
f
(
y
))
=
f
(
x
)
y
+
a
holds for every
x
,
y
∈
R
x, y\in \mathbb{R}
x
,
y
∈
R
.
algebra
TST
functional equation