If our function is
then is defined exactly where is defined and non-negative; that is, where
By two reversible operations, we find that this is equivalent to saying
Therefore, must be positive and must lie in the first or third quadrant. Now, if we knew that were positive, we could divide by to obtain
but in the third quadrant, , and we can't do this without reversing the inequality. In fact, while your answer is correct in the first quadrant, in the third quadrant it will be
Hope this helps!