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Problem
Problem
Let
g
(
x
)
=
f
(
x
)
+
f
(
1
−
x
)
g(x) = f(x) + f(1-x)
g
(
x
)
=
f
(
x
)
+
f
(
1
−
x
)
and
f
′
′
(
x
)
>
0
,
∀
x
∈
(
0
,
1
)
f''(x) > 0, \forall x \in (0, 1)
f
′′
(
x
)
>
0
,
∀
x
∈
(
0
,
1
)
. Then,
g
(
x
)
g(x)
g
(
x
)
is a. increasing on
(
0
,
1
2
)
\left(0, \frac{1}{2}\right)
(
0
,
2
1
)
and decreasing on
(
1
2
,
1
)
\left(\frac{1}{2}, 1\right)
(
2
1
,
1
)
b. increasing on
(
1
2
,
1
)
\left(\frac{1}{2}, 1\right)
(
2
1
,
1
)
and decreasing on
(
0
,
1
2
)
\left(0, \frac{1}{2}\right)
(
0
,
2
1
)
c. increasing on
(
0
,
1
)
(0, 1)
(
0
,
1
)
d. decreasing on
(
0
,
1
)
(0, 1)
(
0
,
1
)
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