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what is the domain of the following? a) y = √sin x b) √(((x-1)(x-5))/(x-3))

what is the domain of the following?
a) y = √sin x            b) √(((x-1)(x-5))/(x-3))

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1 Answers

Y RAJYALAKSHMI
45 Points
8 years ago
a)   √sin x is defined for sinx > =0,  ie. x = [0, pi], [2pi, 3pi], [4pi, 5pi], …. 
In general the domain x = [2n*pi, (2n+1)*pi] where n is an integer
 
b)  √(((x-1)(x-5))/(x-3)) is defined for (((x-1)(x-5))/(x-3)) > = 0
ie.  (((x-1)(x-5))(x-3)) > = 0
x # 3, x = [1,3), x >= 5
 
 
 

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