A function f is defined by f : x → 5 − 2 sin 2x for 0 ≤ x ≤ pi.
Solve the equation f(x) =6 giving answers in terms of pi
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Explanation:
To find the range, proceed as follows :
−
1
≤
sin
x
≤
1
−
1
≤
sin
2
x
≤
1
1
≥
−
sin
2
x
≥
−
1
2
≥
−
2
sin
2
x
≥
−
2
2
+
5
≥
(
5
−
2
sin
2
x
)
≥
−
2
+
5
3
≤
f
(
x
)
=
(
5
−
2
sin
2
x
)
≤
7
Therefore,
the range is
f
(
x
)
∈
[
3
,
7
]
To sketch the graph in the domain
x
∈
(
0
,
π
)
Calculate the following values
a
a
a
a
x
a
a
a
a
f
(
x
)
a
a
a
a
0
a
a
a
a
5
a
a
a
a
π
4
a
a
a
a
3
a
a
a
a
π
2
a
a
a
a
5
a
a
a
a
3
4
π
a
a
a
a
7
a
a
a
a
π
a
a
a
a
5
5
−
2
sin
2
x
=
6
2
sin
2
x
=
−
1
sin
2
x
=
−
1
2
2
x
=
7
π
6
,
⇒
,
x
=
7
12
π
2
x
=
11
6
π
,
⇒
,
x
=
11
12
π
See the graph below
graph{(y-5+2sin(2x))(y-6)=0 [-10, 10, -5, 5]}
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