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If f(x)=sin^2x+sin^2(x+pi/3)+cosxcos(x+p...

If `f(x)=sin^2x+sin^2(x+pi/3)+cosxcos(x+pi/3)a n dg(5/4=1,` then `(gof)(x)` is ____________

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The correct Answer is:
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`f(x)=sin^(2)x+sin^(2)(x+(pi)/(3))+cosxcos(x+(pi)/(3))`
`=sin^(2)x+(1)/(4)(sinx+sqrt(3)cosx)^(2)+(1)/(2)cosx(cosx-sqrt(3)sinx)`
`=(5)/(4)(sin^(2)x+cos^(2)x)=(5)/(4)`
`(gof)x=g[f(x)]=g(5//4)=1`
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CENGAGE-RELATIONS AND FUNCTIONS-Exercise (Numerical)
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  5. An even polynomial function f(x) satisfies a relation f(2x)(1-f(1/(2x)...

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  6. If f(x)=sin^2x+sin^2(x+pi/3)+cosxcos(x+pi/3)a n dg(5/4=1, then (gof)(x...

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  7. Let E={1,2,3,4,} and F={1,2}. Then the number of onto functions from E...

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