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Problems
If
f
(
x
)
=
{
⌊
1
−
4
x
2
⌋
,
0
≤
x
<
1
⌊
x
2
−
2
x
⌋
,
1
≤
x
<
2
f(x) = \begin{cases} \lfloor 1 - 4x^2 \rfloor, & 0 \le x < 1 \\ \lfloor x^2 - 2x \rfloor, & 1 \le x < 2 \end{cases}
f
(
x
)
=
{
⌊
1
−
4
x
2
⌋
,
⌊
x
2
−
2
x
⌋
,
0
≤
x
<
1
1
≤
x
<
2
…
Mathematics
Problem
If
f
(
x
)
=
{
⌊
1
−
4
x
2
⌋
,
0
≤
x
<
1
⌊
x
2
−
2
x
⌋
,
1
≤
x
<
2
f(x) = \begin{cases} \lfloor 1 - 4x^2 \rfloor, & 0 \le x < 1 \\ \lfloor x^2 - 2x \rfloor, & 1 \le x < 2 \end{cases}
f
(
x
)
=
{
⌊
1
−
4
x
2
⌋
,
⌊
x
2
−
2
x
⌋
,
0
≤
x
<
1
1
≤
x
<
2
, where
⌊
⌋
\lfloor\ \rfloor
⌊
⌋
denotes the greatest integer function, then a.
f
(
x
)
f(x)
f
(
x
)
is continuous for all
x
∈
[
0
,
2
]
x \in [0, 2]
x
∈
[
0
,
2
]
b.
f
(
x
)
f(x)
f
(
x
)
is differentiable for all
x
∈
[
0
,
2
]
−
{
1
}
x \in [0, 2] - \{1\}
x
∈
[
0
,
2
]
−
{
1
}
c.
f
(
x
)
f(x)
f
(
x
)
is differentiable for all
x
∈
[
0
,
2
]
−
{
1
2
,
1
}
x \in [0, 2] - \left\{\frac{1}{2}, 1\right\}
x
∈
[
0
,
2
]
−
{
2
1
,
1
}
d. None of these
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