find the domain and range of 3sinx-5/2
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Answer:
f(x)=cos
2
x−5cosx−6
Let cosx=t
⇒f(t)=t
2
−5t−6
Where t=cosx∈[−1,1]
Vertex of quadrate is : (−
2a
b
,−
4a
D
)
For f(t) vertex is : (
2(1)
−(−5)
,
4(1)
−(25−4(−6))
)
:(
2
5
,
4
−49
)
but t can not take value
2
5
as t∈[−1,1]
⇒f(t) will not take value −
4
49
f(1)=1−5−6=−10
f(−1)=1+5−6=0
⇒ For t∈[−1,1], range of f(t) is : Range ∈[−10,0]
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