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Mathematics
Problem
Let
f
f
f
be the continuous and differentiable function such that
f
(
x
)
=
f
(
2
−
x
)
f(x) = f(2-x)
f
(
x
)
=
f
(
2
−
x
)
,
∀
x
∈
R
\forall x \in R
∀
x
∈
R
and
g
(
x
)
=
f
(
1
+
x
)
g(x) = f(1+x)
g
(
x
)
=
f
(
1
+
x
)
, then a.
g
(
x
)
g(x)
g
(
x
)
is an odd function b.
g
(
x
)
g(x)
g
(
x
)
is an even function c.
f
(
x
)
f(x)
f
(
x
)
is symmetric about
x
=
1
x = 1
x
=
1
d. None of the above
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