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Problem
Problem
Let
f
(
x
)
f(x)
f
(
x
)
and
g
(
x
)
g(x)
g
(
x
)
be two continuous functions defined from
R
→
R
R \to R
R
→
R
, such that
f
(
x
1
)
>
f
(
x
2
)
f(x_1) > f(x_2)
f
(
x
1
)
>
f
(
x
2
)
and
g
(
x
1
)
<
g
(
x
2
)
g(x_1) < g(x_2)
g
(
x
1
)
<
g
(
x
2
)
,
∀
x
1
>
x
2
\forall x_1 > x_2
∀
x
1
>
x
2
, then solution set of
f
(
g
(
α
2
−
2
α
)
)
>
f
(
g
(
3
α
−
4
)
)
f(g(\alpha^2 - 2\alpha)) > f(g(3\alpha - 4))
f
(
g
(
α
2
−
2
α
))
>
f
(
g
(
3
α
−
4
))
, then the least value of
α
\alpha
α
for which
f
(
g
(
α
2
−
2
α
)
)
>
f
(
g
(
3
α
−
4
)
)
f(g(\alpha^2 - 2\alpha)) > f(g(3\alpha - 4))
f
(
g
(
α
2
−
2
α
))
>
f
(
g
(
3
α
−
4
))
is .....
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