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Question
Mathematics
The domain of the function f(x) = sin-1((x+5/2)) is
Q. The domain of the function
f
(
x
)
=
s
i
n
−
1
(
2
x
+
5
)
is
3922
221
KEAM
KEAM 2012
Inverse Trigonometric Functions
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A
[-1,1]
16%
B
[2, 3]
13%
C
[3, 7]
13%
D
[-7, -3]
52%
E
(
∞
,
∞
)
52%
Solution:
Given,
f
(
x
)
=
sin
−
1
(
2
x
+
5
)
[
∵
Domain of
sin
−
1
x
is
x
∈
[
−
1
,
1
]
]
∴
For
f
(
x
)
to be defined
−
1
≤
2
x
+
5
≤
1
⇒
−
2
≤
x
+
5
≤
2
⇒
−
2
−
5
≤
x
≤
2
−
5
⇒
−
7
≤
x
≤
−
3
∴
x
∈
[
−
7
,
−
3
]