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Problem
Problem
If
h
(
x
)
=
A
x
3
+
B
sin
x
+
C
ln
(
1
+
x
1
−
x
)
+
7
h(x) = Ax^3 + B \sin x + C \ln\left(\frac{1+x}{1-x}\right) + 7
h
(
x
)
=
A
x
3
+
B
sin
x
+
C
ln
(
1
−
x
1
+
x
)
+
7
, where
A
,
B
,
C
A, B, C
A
,
B
,
C
are non-zero real constants and
h
(
−
1
2
)
=
6
h\left(\frac{-1}{2}\right) = 6
h
(
2
−
1
)
=
6
, then find the value of
h
(
sgn
(
e
−
x
)
2
)
h\left(\frac{\operatorname{sgn}(e^{-x})}{2}\right)
h
(
2
sgn
(
e
−
x
)
)
.
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