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A real-valued function satisfies the functional equation
MATHEMATICS · Subjective · AoPS · Mathematics · Functions · Functions
Problem
A real-valued function
f
(
x
)
f(x)
f
(
x
)
satisfies the functional equation
f
(
x
−
y
)
=
f
(
x
)
f
(
y
)
−
f
(
a
−
x
)
f
(
a
+
y
)
f(x-y)=f(x)f(y)-f(a-x)f(a+y)
f
(
x
−
y
)
=
f
(
x
)
f
(
y
)
−
f
(
a
−
x
)
f
(
a
+
y
)
, where
a
a
a
is a given constant and
f
(
0
)
=
1
f(0)=1
f
(
0
)
=
1
. Find
f
(
2
a
−
x
)
f(2a-x)
f
(
2
a
−
x
)
.
Related theory
Functions
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