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g(x) = x + (1/2) is the probability density function of X, derived by integrating f(x,y) with respect to y, over 0 < y < 1. Since we "took y out of the equation", the support of this function should be 0 < x < 1.

Question :

What is the support of the conditional density function h(y|x) = f(x,y)/g(x)?

My guess is that this function is well defined and takes non zero values only over region {0 < x < 1, 0 < y < 1} and so this is the support.

But the book I am using states 0 < y < 1 instead. Is it a typo?