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Mathematics
Problem
Let
q
(
x
)
=
⌊
x
⌋
2
−
sgn
(
x
)
⌊
x
⌋
q(x)=\lfloor x\rfloor^{2}-\operatorname{sgn}(x)\,\lfloor x\rfloor
q
(
x
)
=
⌊
x
⌋
2
−
sgn
(
x
)
⌊
x
⌋
. The set of real solutions of the equation
q
(
x
)
=
2
q(x)=2
q
(
x
)
=
2
is a)
[
−
2
,
−
1
)
∪
[
1
,
2
)
[-2,-1)\cup[1,2)
[
−
2
,
−
1
)
∪
[
1
,
2
)
b)
(
−
2
,
−
1
]
∪
[
2
,
3
)
(-2,-1]\cup[2,3)
(
−
2
,
−
1
]
∪
[
2
,
3
)
c)
[
−
2
,
−
1
)
∪
[
2
,
3
)
[-2,-1)\cup[2,3)
[
−
2
,
−
1
)
∪
[
2
,
3
)
d)
[
−
1
,
0
)
∪
[
2
,
3
)
[-1,0)\cup[2,3)
[
−
1
,
0
)
∪
[
2
,
3
)
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