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Byju's Answer
Standard XII
Mathematics
Range
If a function...
Question
If a function
f
:
[
−
2
,
∞
)
→
R
is such that
f
(
x
)
=
x
2
+
4
x
−
|
x
2
−
4
|
, then the value(s)
f
(
x
)
can have is (are)
A
−
6
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B
−
8
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C
4
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D
0
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Solution
The correct options are
A
−
6
C
4
D
0
f
(
x
)
=
{
2
x
2
+
4
x
−
4
,
x
∈
[
−
2
,
2
]
4
x
+
4
x
∈
(
2
,
∞
)
So, the range
=
[
−
6
,
∞
)
Suggest Corrections
0
Similar questions
Q.
If a function
f
:
[
−
2
,
∞
)
→
R
is such that
f
(
x
)
=
x
2
+
4
x
−
|
x
2
−
4
|
,
then the value(s)
f
(
x
)
can have is (are)
Q.
Let
f
:
R
→
R
be a continuous function such that
f
(
x
)
−
2
f
(
x
2
)
+
f
(
x
4
)
=
x
2
f
′
(
0
)
is equal to :
Q.
If a function from
R
→
R
such that
f
(
x
)
=
x
2
∀
x
ϵ
R
then show that f is not one-one.
Q.
Given
f
:
[
0
,
∞
)
→
R
be a strictly increasing function such that the functions
g
(
x
)
=
f
(
x
)
−
3
x
and
h
(
x
)
=
f
(
x
)
−
x
3
are both strictly increasing function. Then the function
F
(
x
)
=
f
(
x
)
−
x
2
−
x
is
Q.
Let
f
:
R
→
R
be a continuous function such that
f
(
x
)
−
2
f
(
x
2
)
+
f
(
x
4
)
=
x
2
The equation
f
(
x
)
−
x
−
f
(
0
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=
0
have exactly :
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