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UPSC NDA 2 2016 Mathematics Solved Paper
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© examsnet.com
Question : 71
Total: 120
What is the domain of the function
f
(
x
)
=
1
√
|
x
|
−
x
?
[NDA II 2016]
(
−
∞
,
0
)
(
0
,
∞
)
0 < x < 1
x
>
1
Validate
Solution:
We know that
|
x
|
=
{
x
,
x
≥
0
−
x
,
x
<
0
For domain,
|
x
|
−
x
>
0
Case 2:
x
Case 1:
x
>
0
⇒
x
−
x
=
0
(not possible)
−
x
−
x
>
0
⇒
−
2
x
>
0
⇒
x
<
0
So,
x
∊
(
−
∞
,
0
)
© examsnet.com
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