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Mathematics
Mathematics
Problem
Discuss the continuity of
f
f
f
in
[
0
,
2
]
[0, 2]
[
0
,
2
]
, where
f
(
x
)
=
{
∣
4
x
−
5
∣
[
x
]
,
for
x
>
1
,
[
cos
π
x
]
,
for
x
≤
1
,
f(x)=\begin{cases} |4x-5|[x], & \text{for } x>1,\\ [\cos \pi x], & \text{for } x\le 1, \end{cases}
f
(
x
)
=
{
∣4
x
−
5∣
[
x
]
,
[
cos
π
x
]
,
for
x
>
1
,
for
x
≤
1
,
where
[
x
]
[x]
[
x
]
is greatest integer not greater than
x
x
x
.
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