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Mathematics
Mathematics
Problem
If
f
(
x
)
=
{
sin
π
x
2
,
x
<
1
[
x
]
,
x
≥
1
f(x) = \begin{cases} \sin \frac{\pi x}{2}, & x < 1 \\ [x], & x \ge 1 \end{cases}
f
(
x
)
=
{
sin
2
π
x
,
[
x
]
,
x
<
1
x
≥
1
, where
[
x
]
[x]
[
x
]
denotes the greatest integer function, then a.
f
(
x
)
f(x)
f
(
x
)
is continuous at
x
=
1
x=1
x
=
1
b.
f
(
x
)
f(x)
f
(
x
)
is discontinuous at
x
=
1
x=1
x
=
1
c.
f
(
1
+
)
=
0
f(1^+) = 0
f
(
1
+
)
=
0
d.
f
(
1
−
)
=
−
1
f(1^-) = -1
f
(
1
−
)
=
−
1
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