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Aakash Verma's Avatar
Aakash Verma
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Joined: 6 May 2011
Post: 102
7 May 2011 20:58:34 IST
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The function f : R ? R is defined f(x) = cos^2x + sin^4x. What is the range of f ? Please show th
Engineering Entrance , JEE Main , JEE Advanced , Mathematics , Algebra

The function f : R ? R is defined f(x) = cos^2x + sin^4x. What is the range of f ? Please show the calculation.


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GOPAKUMAR
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9 May 2011 07:55:07 IST
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 f(x)=Cos2x+sin4x =1- sin2x+ sin4x

                       Put  sin2x=t

Then

f(x)=1-t+t2

now since sin2x €[0,1] therefore t€[0,1]

therefore f(x) €[3/4,1]   since for  t€[0,1] the max & min value of f(x) are 1 & 3/4  at t=1/2 & t=1or0 respectively
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GOPAKUMAR
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9 May 2011 07:56:11 IST
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 therefore Range of f is[3/4,1] 
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