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Byju's Answer
Standard XII
Mathematics
Range of Quadratic Expression
Range of the ...
Question
Range of the expression
f
(
x
)
=
x
2
+
x
+
1
x
2
−
x
+
1
,
x
∈
R
is
A
[
1
3
,
3
]
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B
(
−
∞
,
1
3
]
∪
[
3
,
∞
)
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C
(
1
3
,
3
)
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D
R
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Solution
The correct option is
A
[
1
3
,
3
]
Let
y
=
x
2
+
x
+
1
x
2
−
x
+
1
⇒
y
x
2
−
y
x
+
y
=
x
2
+
x
+
1
⇒
(
y
−
1
)
x
2
−
(
y
+
1
)
x
+
(
y
−
1
)
=
0
∵
x
∈
R
⇒
Δ
≥
0
⇒
(
y
+
1
)
2
−
4
(
y
−
1
)
2
≥
0
⇒
−
3
y
2
+
10
y
−
3
≥
0
⇒
3
y
2
−
10
y
+
3
≤
0
⇒
(
3
y
−
1
)
(
y
−
3
)
≤
0
⇒
y
∈
[
1
3
,
3
]
Suggest Corrections
0
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Range of Quadratic Expression
Standard XII Mathematics
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