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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
and let
g
(
x
)
=
f
(
∣
x
∣
)
+
∣
f
(
x
)
∣
g(x) = f(|x|) + |f(x)|
g
(
x
)
=
f
(
∣
x
∣
)
+
∣
f
(
x
)
∣
. Discuss the differentiability of
g
(
x
)
g(x)
g
(
x
)
.
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