Question

xy-y^2=1?
give the domain and the range

Answer 1

domain x ≤ -2 or x ≥2
range (-infinity,0)(0,infinity)

Answer 2

Equation becomes: y^2 - xy = -1. Completing the square, we eventually get:\[y = \frac{ x }{ 2 }\pm \sqrt{\frac{ x ^{2} }{ 4 }-1}\]Now, couple things can be said right off about this. First thing is that you have a relation, not an equation, since you have the "+-", so you can break this up into the "+" and the "-" for two branches, each of which by itself is an equation. Second, you cannot have -2 < x < +2, but all other x are okay. Third, we now consider the range.

Answer 3

When we have the "+" branch, we get for "y" that [-1, 0) and [1, inf). When we look at the "-" branch we get for "y" that (-inf, -1] and (0, 1]. So, the total range is (-inf, 0) and (0, inf) which is everything except 0 for the range.

Answer 4

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