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Find Domain of the rational

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David,
 
f(x) means that the function is in terms of x, but you're saying that the function f(x) is:
 
f(x) = (y+2)/(y2 - 2y)
 
which is in terms of y.  So it should be either f(y) or f(x) = (x+2)/(x2 - 2x).
 
Domain, by definition, is a set of values in which the function is "defined".
 
First, factor the denominator x2 - 2x, which is x(x-2). And we know that denominators cannot be zero (or else the function is "undefined").  So this means that the value(s) of x that make(s) the function undefined is when...
 
x(x-2) = 0
 
This is true when x = 2 and when x = 0.
 
So the domain of the function is all values of x except when x = {0,2}. To write this is notation form D = (-infinity∪0∪2∪infinity).
 
I hope that helps! :)