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Byju's Answer
Standard XII
Mathematics
Range
Let f : R → R...
Question
Let
f
:
R
→
R
be defined by
f
(
x
)
=
x
1
+
x
2
,
x
∈
R
.
Then the range of
f
is
A
R
−
[
−
1
2
,
1
2
]
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B
R
−
[
−
1
,
1
]
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C
(
−
1
,
1
)
−
{
0
}
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D
[
−
1
2
,
1
2
]
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Solution
The correct option is
D
[
−
1
2
,
1
2
]
f
(
x
)
=
x
1
+
x
2
,
x
∈
R
Let
y
=
f
(
x
)
∴
y
=
x
1
+
x
2
⇒
y
x
2
−
x
+
y
=
0
⇒
x
=
1
±
√
1
−
4
y
2
2
y
For
x
to be defined,
1
−
4
y
2
≥
0
,
y
≠
0
⇒
y
∈
[
−
1
2
,
1
2
]
−
{
0
}
But for
x
=
0
,
y
=
0
∴
R
(
f
)
=
[
−
1
2
,
1
2
]
Suggest Corrections
128
Similar questions
Q.
Let
f
:
R
→
R
be defined by
f
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x
)
=
x
1
+
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2
,
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Q.
Let
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Let
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Range
Standard XII Mathematics
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