Nontrivial functions $f$ and $g$ Give an example of two nontrivial functions $f$ and $g$ such that $$(f \circ g)(x) = \sqrt{x^2 - 1}$$
where $f(x)=$ ?  and $g(x)=$ ?
My answer is $f(x)=\mathrm{sqrt}(x)$ and $g(x)=x^2-1$. But this seems to not be the right answer? Help please.

Yours works just fine (as you've discovered), but it's worth noting that there are many other ways we could define such $f,g$. The simplest alternative is probably $f(x)=\sqrt{x-1}$ and $g(x)=x^2,$ but for any real $r$, the functions $f(x)=\sqrt{x+r-1}$ and $g(x)=x^2-r$ will also do the job.
