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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 the greatest integral function and
I
I
I
is the set of integers. Find
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
.
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