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Byju's Answer
Standard XII
Mathematics
Method of Intervals
The domain of...
Question
The domain of the function
f
(
x
)
=
1
√
(
[
x
]
2
−
7
[
x
]
+
10
)
is
(
−
∞
,
a
)
∪
[
b
,
∞
)
,
then
a
+
b
is
(
[
x
]
denotes the greatest integer less than or equal to
x
)
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Solution
For
f
(
x
)
to be defined,
[
x
]
2
−
7
[
x
]
+
10
>
0
⇒
(
[
x
]
−
5
)
(
[
x
]
−
2
)
>
0
⇒
[
x
]
∈
(
−
∞
,
2
)
∪
(
5
,
∞
)
∴
x
∈
(
−
∞
,
2
)
∪
[
6
,
∞
)
Clearly,
a
=
2
;
b
=
6
So
a
+
b
=
8
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16
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