Hi, I'm trying to understand the example the book gives:

For the functions $\displaystyle f(x)=x^2-1, x \in R,$ and $\displaystyle g(x) = \sqrt{x},x \geq 0$, state why $\displaystyle g(f(x))$ is not defined.

Range of $\displaystyle f \not\subseteq$ domain of g.

Therefore, g(f(x)) is not defined.

How can it not be defined? I've drawn graphs of $\displaystyle y = \sqrt{x^2-1}$ and they look perfectly reasonable. What is going on? Thanks