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Mathematics
Mathematics
Problem
5. Determine the domain of the function
f
(
x
)
=
arcsin
(
2
x
−
1
x
+
2
)
f(x)=\arcsin\!\left(\dfrac{2x-1}{x+2}\right)
f
(
x
)
=
arcsin
(
x
+
2
2
x
−
1
)
. a)
(
−
1
3
,
3
]
(-\tfrac{1}{3},\,3]
(
−
3
1
,
3
]
b)
(
−
∞
,
−
2
)
∪
[
−
1
3
,
3
]
(-\infty,-2)\;\cup\;[-\tfrac{1}{3},\,3]
(
−
∞
,
−
2
)
∪
[
−
3
1
,
3
]
c)
[
−
1
3
,
3
]
\bigl[-\tfrac{1}{3},\,3\bigr]
[
−
3
1
,
3
]
d)
(
−
2
,
3
]
(-2,\,3]
(
−
2
,
3
]
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