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If `f(x)=sqrt(4-x^2)+sqrt(x^2-1)`, then the maximum value of `(f(x))^2`is ____________ |
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Answer» Correct Answer - 6 Let `x^(2)=4cos^(2) theta+sin^(2) theta.` Then `(4-x^(2))=3 sin^(2) theta and (x^(2)-1)=3 cos^(2)theta` ` :. f(x)=sqrt(3)|sin theta|+sqrt(3)|cos theta|` `or y_(min)=sqrt(3) and y_(max)=sqrt(3)((1)/(sqrt(2))+(1)/(sqrt(2)))=sqrt(6)` Hence, range of `f(x) " is " [sqrt(3),sqrt(6)].` Hence, maximum value of `(f(x))^(2) ` is 6. |
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