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  • Find the domain of f(x)=square root sin x + square root (16-x^2) .

Find the domain of f(x)=square root sin x + square root (16-x^2) .

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Solution:   We have ,   f(x)=sqrtsin x+sqrt(16-x^2)

               For     sqrt(16-x^2)Rightarrow 16-x^2geq 0

             Rightarrow              -4leq xleq 4     

              For      sqrtsin xRightarrow sin xgeq 0Rightarrow 2npileq xleq (2n+1)pi

             Thus , taking intersection with  -4leq xleq 4 we get [-4,-pi]cup [0,pi].

Posted by

Deependra Verma

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