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Byju's Answer
Standard XII
Mathematics
Theorems for Differentiability
The domain of...
Question
The domain of the function,
f
(
x
)
=
√
2
−
x
−
1
√
9
−
x
2
is
A
(-3,1)
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B
[-3,1]
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C
(-3,2)
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D
(-3,2]
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Solution
The correct option is
D
(-3,2]
Given,
f
(
x
)
=
√
2
−
x
−
1
√
9
−
x
2
√
f
(
x
)
⇒
f
(
x
)
≥
0
2
−
x
≥
0
:
x
≤
2
9
−
x
2
≥
0
:
−
3
≤
x
≤
3
Combined interval:
−
3
≤
x
≤
2
Undefined singularity points:
x
=
3
,
x
=
−
3
Combining real regions and undefined singularity points:
−
3
<
x
≤
2
(
−
3
,
2
]
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