Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Problem
Problem
If the range of the function
f
(
x
)
=
{
x
4
}
+
cos
π
(
(
1
−
2
[
x
]
)
2
)
+
sin
(
π
[
x
]
2
)
f(x)=\left\{\frac{x}{4}\right\}+\cos\pi\left(\frac{(1-2[x])}{2}\right)+\sin\left(\frac{\pi[x]}{2}\right)
f
(
x
)
=
{
4
x
}
+
cos
π
(
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
Browse the problem library