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Mathematics
Mathematics
Problem
Let
f
:
R
→
[
0
,
2
π
3
]
f: \mathbb{R} \to \left[0, \frac{2\pi}{3}\right]
f
:
R
→
[
0
,
3
2
π
]
be defined as
f
(
x
)
=
cot
−
1
(
x
2
−
4
x
+
α
)
f(x) = \cot^{-1}(x^2 - 4x + \alpha)
f
(
x
)
=
cot
−
1
(
x
2
−
4
x
+
α
)
. Find the smallest integral value of
α
\alpha
α
such that
f
(
x
)
f(x)
f
(
x
)
is an into function.
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