How do you find domain for $y = sqrt((4+x) / (1-x) )$ ?

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Answer 1 · 2015-09-27T09:21:16

Domain ${x:RR, -4<=x<1}$

Range ${y:RR, y>=0]$

For real y, $4+x>=0, x>=-4$ ; and $1-x>0, or, x<1$

The domain is therefore ${x:RR, -4<=x<1}$

For range, at x=-4, y is 0 and as x increases from -4, y remains positive and as x approaches 1, $y->+oo$ . Hence Range would be

${y:RR, y>=0}$

How do you find domain for y = sqrt((4+x) / (1-x) ) y = sqrt((4+x) / (1-x) ) ?