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Mathematics
Mathematics
Problem
Let
f
(
x
)
=
−
x
3
+
x
2
−
x
+
1
f(x) = -x^3 + x^2 - x + 1
f
(
x
)
=
−
x
3
+
x
2
−
x
+
1
and
g
(
x
)
=
{
min
0
≤
t
≤
x
f
(
t
)
,
0
≤
x
≤
1
x
−
1
,
1
<
x
≤
2
g(x) = \begin{cases} \min_{0 \le t \le x} f(t), & 0 \le x \le 1 \\ x-1, & 1 < x \le 2 \end{cases}
g
(
x
)
=
{
min
0
≤
t
≤
x
f
(
t
)
,
x
−
1
,
0
≤
x
≤
1
1
<
x
≤
2
Then, the value of
lim
x
→
1
g
(
g
(
x
)
)
\lim_{x \to 1} g(g(x))
lim
x
→
1
g
(
g
(
x
))
, is.....
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