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Let for all and
MATHEMATICS · Single correct · AoPS · Mathematics · Functions · Functions
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
f
(
f
′
(
0
)
)
f\bigl(f'(0)\bigr)
f
(
f
′
(
0
)
)
is (1)
−
1
-1
−
1
(2)
0
0
0
(3)
1
1
1
(4)
2
2
2
Related theory
Differentiation Rules
Functions
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