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Mathematics
Mathematics
Problem
Consider the function
f
(
x
)
=
{
x
−
[
x
]
−
1
2
,
if
x
∉
I
0
,
if
x
∈
I
,
where
[
.
]
denotes the greatest integer function and
I
is the set of integers.
f(x) = \begin{cases} x - [x] - \frac{1}{2}, & \text{if } x \notin I \\ 0, & \text{if } x \in I \end{cases}, \text{ where } [.] \text{ denotes the greatest integer function and } I \text{ is the set of integers.}
f
(
x
)
=
{
x
−
[
x
]
−
2
1
,
0
,
if
x
∈
/
I
if
x
∈
I
,
where
[
.
]
denotes the greatest integer function and
I
is the set of integers.
If
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
, then find the area bounded by
g
(
x
)
g(x)
g
(
x
)
when
−
2
≤
x
≤
2
-2 \le x \le 2
−
2
≤
x
≤
2
.
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