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Differential Calculus

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15 Jun 2012 17:03:52 IST

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Domain And Range

Engineering Entrance , JEE Main , JEE Advanced , Mathematics , Differential Calculus

Consider the real valued function satisfying 2f (sin x) + f (cos x) = x . Find domain And Range of f(x).

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Sagar Saxena

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Joined: 8 Oct 2008

Posts: 8064

16 Jun 2012 14:15:39 IST

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see we can give any value to x here so the domain would be r

put x=sin^-1x

2f(x)+f((1-x^2)^1/2)=sin^-1x

put x=cos^-1x

2f((1-x^2)^0.5)+f(x)=cos^-1x

solve these equation

F(x)=(2sin-1x-cos^-1x)/3

F(x)=(pi-3*cos^-1x)/3

range would be(-2*pi/3,pi/3)

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