Find the domain of the funtion f(x) = sin inverse (2x-3)
Answers
Answer:
nswer:
x
∈
[
−
2
,
−
1
]
and
y
∈
[
−
π
2
,
π
2
]
, for this truncated graph.
Explanation:
g
(
x
)
=
sin
−
1
(
2
x
+
3
)
.
This is one-piece inverse with
g
∈
[
−
π
2
,
π
2
]
of
x
=
1
2
(
sin
g
−
3
)
.
Correspondingyt, the domain is given by
x
∈
[
1
2
(
sin
(
−
π
2
)
−
3
)
,
1
2
(
sin
(
π
2
)
−
3
)
=
[
−
2
,
−
1
]
.
See illustrative graph, within the enclosure
x
=
−
2
,
y
=
π
2
,
x
=
−
1
and
y
=
−
π
2
o.
graph{(y - arcsin ( 2 x + 3 ))(y^2-(pi/2)^2) = 0[-3 0 -2 2]}
For information, the wholesome graph for
g
=
(
sin
)
−
1
(
2
x
+
3
)
, using the inverse
x
=
1
2
sin
(
(
g
)
−
3
)
is shown below.
graph{x-1/2( sin (y) - 3 ) = 0 [-3 0 -10 10]}
Here, g-range is without limit.
I use
(
sin
)
−
1
for the wholesome inverse. This enables me to
reveal more details..
Step-by-step explanation:
Answer:
Step-by-step explanation:
