<s>[INST] Domain of functions that involve composition Suppose the domain of $f$ is $(-1,1)$. Define the function $\ell$ by
$$\ell(x)=f\left(\frac{x+1}{x-1}\right).$$ What is the domain of l
 [/INST] As pointed in the comments, you want to solve: $$-1< \frac{x+1}{x-1} < 1$$for $x$. Rewrite $\frac{x+1}{x-1} = 1 + \frac{2}{x-1}$, so that: $$-1< \frac{x+1}{x-1} < 1 \implies -1 < 1 + \frac{2}{x-1} < 1 \implies -1 < \frac{1}{x-1} < 0.$$Can you solve that last one now?
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