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Problem
Problem
If the range of the function
f
(
x
)
=
{
x
4
}
+
cos
π
f(x) = \left\{\frac{x}{4}\right\} + \cos \pi
f
(
x
)
=
{
4
x
}
+
cos
π
(
(
1
−
2
[
x
]
)
2
)
+
sin
(
π
[
x
]
2
)
\left(\frac{(1-2[x])}{2}\right) + \sin\left(\frac{\pi[x]}{2}\right)
(
2
(
1
−
2
[
x
])
)
+
sin
(
2
π
[
x
]
)
is
[
α
4
,
β
4
]
∪
[
γ
4
,
δ
4
]
∪
[
2
γ
+
1
4
,
δ
2
]
\left[\frac{\alpha}{4}, \frac{\beta}{4}\right] \cup \left[\frac{\gamma}{4}, \frac{\delta}{4}\right] \cup \left[\frac{2\gamma+1}{4}, \frac{\delta}{2}\right]
[
4
α
,
4
β
]
∪
[
4
γ
,
4
δ
]
∪
[
4
2
γ
+
1
,
2
δ
]
, (where
{
.
}
\{.\}
{
.
}
and
[
.
]
[.]
[
.
]
represent fractional part and greatest integer part functions respectively), then
α
2
+
β
2
+
γ
2
+
δ
2
\alpha^2 + \beta^2 + \gamma^2 + \delta^2
α
2
+
β
2
+
γ
2
+
δ
2
is
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