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Q.

Let f:X→Y, f(x)=Sinx+Cosx+22  is invertible, then X→Y  is/are

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a

[π4,5π4]→[2,32]

b

[−π4,3π4]→[2,32]

c

[−3π4,3π4]→[2,32]

d

[−3π4,−π4]→[2,32]

answer is A.

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Detailed Solution

f(x)=2Sinx(x+π4)+22 ⇒f(x)=2Cos(x−π4)+22 ⇒Y=[2,32] and X=[−3π4,π4] Or [π4,5π4]
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Let f:X→Y, f(x)=Sinx+Cosx+22  is invertible, then X→Y  is/are