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Mathematics
Mathematics
Problem
Let
f
(
x
+
y
)
=
f
(
x
)
+
f
(
y
)
−
2
x
y
−
1
f(x + y) = f(x) + f(y) - 2xy - 1
f
(
x
+
y
)
=
f
(
x
)
+
f
(
y
)
−
2
x
y
−
1
for all
x
x
x
and
y
y
y
. If
f
′
(
0
)
f'(0)
f
′
(
0
)
exists and
f
′
(
0
)
=
−
sin
α
f'(0) = -\sin\alpha
f
′
(
0
)
=
−
sin
α
, then find
f
{
f
(
0
)
}
f\{f(0)\}
f
{
f
(
0
)}
.
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