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Byju's Answer
Standard XII
Mathematics
Continuity of a Function
Which one of ...
Question
Which one of the following graph of the function are continuous interval
[
−
1
,
1
]
A
f
(
x
)
=
{
−
x
2
i
f
−
1
≤
x
<
0
x
2
i
f
0
≤
x
≤
1
}
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B
f
(
x
)
=
⎧
⎨
⎩
1
i
f
−
1
≤
x
<
0
1
x
i
f
x
=
0
⎫
⎬
⎭
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C
both A and B
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D
none of these
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Solution
The correct option is
A
f
(
x
)
=
{
−
x
2
i
f
−
1
≤
x
<
0
x
2
i
f
0
≤
x
≤
1
}
lim
x
→
0
+
f
(
x
)
=
lim
x
→
0
+
x
2
=
0
lim
x
→
0
−
f
(
x
)
=
lim
x
→
0
−
−
x
2
=
0
Hence
L
H
L
=
R
H
L
at 0.
Hence the function is continuous in the interval
[
−
1
,
1
]
.
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0
Similar questions
Q.
The function f(x) is defined as follows f(x) =
⎧
⎨
⎩
−
x
if
x
<
0
x
2
if
0
≤
x
≤
1
t
h
e
n
f
(
x
)
i
s
x
3
−
x
+
1
if
x
>
1
Q.
Let
f
x
=
1
x
for
x
≥
1
a
x
2
+
b
for
x
<
1
If f (x) is continuous and differentiable at any point, then
(a)
a
=
1
2
,
b
=
-
3
2
(b)
a
=
-
1
2
,
b
=
3
2
(c) a = 1, b = − 1
(d) none of these
Q.
If
f
x
=
1
-
1
-
x
2
,
then
f
x
is
(a) continuous on [−1, 1] and differentiable on (−1, 1)
(b) continuous on [−1, 1] and differentiable on
-
1
,
0
∪
0
,
1
(c) continuous and differentiable on [−1, 1]
(d) none of these
Q.
If
f
(
x
)
=
x
2
−
1
, determine which of the following statement(s) is (are) true on the following interval
[
0
,
π
]
.
Q.
Which of the following functions from
A
=
x
∈
R
:
-
1
≤
x
≤
1
to itself are bijections?
(a)
f
x
=
|
x
|
(b)
f
x
=
sin
π
x
2
(c)
f
x
=
sin
π
x
4
(d) None of these
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