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Mathematics
Mathematics
Problem
Let
f
:
(
−
5
,
5
)
→
R
f:(-5,5)\to\mathbb{R}
f
:
(
−
5
,
5
)
→
R
be a differentiable function with
f
(
4
)
=
1
f(4)=1
f
(
4
)
=
1
,
f
′
(
4
)
=
1
f'(4)=1
f
′
(
4
)
=
1
,
f
(
0
)
=
−
1
f(0)=-1
f
(
0
)
=
−
1
and
f
′
(
0
)
=
1
f'(0)=1
f
′
(
0
)
=
1
. If
g
(
x
)
=
(
f
(
2
f
2
(
x
)
+
2
)
)
2
g(x)=(f(2f^2(x)+2))^2
g
(
x
)
=
(
f
(
2
f
2
(
x
)
+
2
)
)
2
, then
−
g
′
(
0
)
-g'(0)
−
g
′
(
0
)
equals
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