What is the domain and range of $y= (sqrt (x+4))/x$ ?

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Answer 1 · 2015-11-03T14:32:26

$x\in[-4,0)uu(0,oo)$
$yin(-oo,oo)$

$x$ cannot be less than -4 due to square root of a negative number.
$x$ cannot be zero due to division by zero.

When $-4<=x<0$ , $-oo<\y<=0$ .
When $0<\x<\oo$ , $0<\y<\oo$ .

What is the domain and range of y= (sqrt (x+4))/xy= (sqrt (x+4))/x?