Question

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

Answer 1

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

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

Explanation:

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}`