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Byju's Answer
Standard XII
Mathematics
Theorems for Continuity
Suppose fx ...
Question
Suppose
f
(
x
)
is piece wise defined by
f
(
x
)
=
⎧
⎨
⎩
2
i
f
x
∈
[
−
3
,
0
)
e
x
i
f
x
∈
[
0
,
2
]
3
x
−
2
i
f
x
∈
(
2
,
∞
)
What is
f
(
−
2
)
?
A
2
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B
4
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C
3
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D
0
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Solution
The correct option is
D
2
Clearly when
x
=
−
2
it lies in first domain and hence
f
(
−
2
)
=
2
Suggest Corrections
0
Similar questions
Q.
Suppose
f
(
x
)
is piece wise defined by
f
(
x
)
=
{
x
+
1
i
f
x
∈
(
−
∞
,
2
)
x
+
3
i
f
x
∈
[
2
,
∞
)
What is
f
(
2
)
?
Q.
Suppose
f
(
x
)
is piece wise defined by
f
(
x
)
=
{
x
+
1
i
f
x
∈
(
−
∞
,
2
)
x
+
3
i
f
x
∈
[
2
,
∞
)
What is
f
(
10
)
?
Q.
If f
:
R
→
R is defined by
f
(
x
)
=
⎧
⎪ ⎪ ⎪
⎨
⎪ ⎪ ⎪
⎩
x
+
2
x
2
+
3
x
+
2
i
f
x
∈
R
−
{
−
1
,
−
2
}
−
1
i
f
x
=
−
2
0
i
f
x
=
−
1
then f is continuous on the set.
Q.
For what value of
k
is the following function continuous at
x
=
2
?
f
(
x
)
=
⎧
⎨
⎩
2
x
+
1
,
k
,
3
x
−
1
,
if
x
<
2
if
x
=
2
if
x
>
2
Q.
Let
X
=
{
x
ϵ
R
|
x
≠
−
3
}
. Let
f
:
X
→
R
be a function defined as
f
(
x
)
=
⎧
⎪ ⎪ ⎪
⎨
⎪ ⎪ ⎪
⎩
x
3
−
27
x
2
−
9
i
f
x
≠
3
9
2
i
f
x
=
3
Then
f
is
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