Question

All real numbers except y=-1

Answer 1

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) = $\frac{1}{x} + 1$

We know that $\frac{1}{x}$, 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.

(fog)(x) = 0 + 1

(fog)(x) = 1

Therefore, y = 1 is the answer.