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Mathematics
Mathematics
Problem
Consider the function
f
(
x
)
=
{
x
−
[
x
]
−
1
2
,
if
x
∉
I
0
,
if
x
∈
I
f(x) = \begin{cases} x - [x] - \frac{1}{2}, & \text{if } x \notin I \\ 0, & \text{if } x \in I \end{cases}
f
(
x
)
=
{
x
−
[
x
]
−
2
1
,
0
,
if
x
∈
/
I
if
x
∈
I
where
[
⋅
]
[\cdot]
[
⋅
]
denotes greatest integer function and
I
I
I
is the set of integers, then
g
(
x
)
=
max
{
x
2
,
f
(
x
)
,
∣
x
∣
}
g(x) = \max\{x^2, f(x), |x|\}
g
(
x
)
=
max
{
x
2
,
f
(
x
)
,
∣
x
∣
}
,
−
2
≤
x
≤
2
-2 \le x \le 2
−
2
≤
x
≤
2
is defined as a.
x
2
x^2
x
2
,
−
2
≤
x
≤
−
1
-2 \le x \le -1
−
2
≤
x
≤
−
1
b.
1
−
x
1 - x
1
−
x
,
−
1
<
x
≤
−
1
4
-1 < x \le -\frac{1}{4}
−
1
<
x
≤
−
4
1
c.
1
2
+
x
\frac{1}{2} + x
2
1
+
x
,
−
1
4
<
x
<
0
-\frac{1}{4} < x < 0
−
4
1
<
x
<
0
d.
1
+
x
1 + x
1
+
x
,
0
≤
x
<
1
0 \le x < 1
0
≤
x
<
1
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