Y = COS-1 2x+1 212x Domain of defin...
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Y = COS-1 2x+1 212x Domain of definition

JEE/Engineering Exams
Maths
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( begin{aligned} y=& cos ^{-1}left(frac{2 x+1}{2 sqrt{2 x}}right) &-1 leqslant frac{2 x+1}{2 sqrt{2 x} leq 1} end{aligned} ) ( 2 sqrt{2 x} eq 0 ) ( frac{2 x+1}{2 sqrt{2 x}} geqslant-1 quad frac{2 x+1^{frac{2 x+1}{2 sqrt{2 x}}} leq 1}{(2 x+1)^{2} leq 8 x} ) ( 2 x+1 geq-2 sqrt{2} x quad 4 x^{2}+1+4 x leq 8 x ) ( 2 x+2 sqrt{2 x}+1 geqslant 0 ) This is always True for every ( x>0 ) ( therefore quad D operatorname{omain} quad f quad f(x)=cos ^{-1}left(frac{2 t+1}{2 sqrt{2 x}}right) ) ( x in{1 / 2} )
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