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Problems
Mathematics
Mathematics
Problem
If
f
(
x
)
=
{
x
−
3
,
x
<
0
x
2
−
3
x
+
2
,
x
≥
0
f(x) = \begin{cases} x - 3, & x < 0 \\ x^2 - 3x + 2, & x \ge 0 \end{cases}
f
(
x
)
=
{
x
−
3
,
x
2
−
3
x
+
2
,
x
<
0
x
≥
0
, then
g
(
x
)
=
f
(
∣
x
∣
)
g(x) = f(|x|)
g
(
x
)
=
f
(
∣
x
∣
)
is a.
g
′
(
0
+
)
=
−
3
g'(0^+) = -3
g
′
(
0
+
)
=
−
3
b.
g
′
(
0
−
)
=
−
3
g'(0^-) = -3
g
′
(
0
−
)
=
−
3
c.
g
′
(
0
+
)
=
g
′
(
0
−
)
g'(0^+) = g'(0^-)
g
′
(
0
+
)
=
g
′
(
0
−
)
d.
g
(
x
)
g(x)
g
(
x
)
is not continuous at
x
=
0
x = 0
x
=
0
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