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Mathematics
Problem
Let
g
(
t
)
=
∣
t
−
1
∣
−
∣
t
∣
+
∣
t
+
1
∣
,
∀
t
∈
R
g(t) = |t - 1| - |t| + |t + 1|,\ \forall t \in \mathbb{R}
g
(
t
)
=
∣
t
−
1∣
−
∣
t
∣
+
∣
t
+
1∣
,
∀
t
∈
R
. Find
f
(
x
)
=
max
{
g
(
t
)
:
−
3
2
≤
t
≤
x
}
,
∀
x
∈
(
−
3
2
,
∞
)
f(x) = \max \{g(t) : -\frac{3}{2} \le t \le x\},\ \forall x \in \left(-\frac{3}{2}, \infty\right)
f
(
x
)
=
max
{
g
(
t
)
:
−
2
3
≤
t
≤
x
}
,
∀
x
∈
(
−
2
3
,
∞
)
.
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