The correct answer is all real numbers except y = 1.
There are two ways of finding this. The first way is by looking at the graph for a value which y never equals. If you look, there are no places where either part of the graph hits y = 1.
The second way is by looking at the combined equation.
(fog)(x) = [tex] \frac{1}{x} + 1 [/tex]
We know that [tex] \frac{1}{x}[/tex], no matter what we put in can ever equal 0. Since that is true, we know y can never equal the number for when that equals 0. So plug in 0 and see what the asymptote is.
