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.
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$\begingroup$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.
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