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The problem is as follows:

Let $f(x) = \frac{1}{1-x} $ for $x \in\mathbb{R}\setminus \{0,1\}. $ Find $(f \circ f)(x)$.

My approach:

$$\begin{align}f\left(\frac{1}{1-x}\right) &= \frac{1}{1 -\frac{1}{1-x}}\\\\ &= \frac{1}{\frac{1-x}{1-x} - \frac{1}{1-x}}\\\\ &=\frac{1}{\frac{-x}{1-x}}\\\\ &=\frac{1-x}{-x}\end{align}$$

But the answer I get is wrong, I'm wondering what did I do wrong?

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    $\begingroup$ Your answer is correct. It’s equal to $\frac{x-1}{x}$, by multiplying the numerator and denominator by $-1$. $\endgroup$
    – Loobear23
    Apr 9, 2021 at 21:45
  • $\begingroup$ @Loobear23 why would I multiply by -1 ? $\endgroup$
    – KetDog
    Apr 9, 2021 at 21:46
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    $\begingroup$ Well, you don’t need to. What is it that makes you think your answer is wrong? $\endgroup$
    – Loobear23
    Apr 9, 2021 at 21:47
  • $\begingroup$ @Papaya-Automaton what is the given answer (in case you know it)? $\endgroup$ Apr 9, 2021 at 21:47
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    $\begingroup$ $\frac{x-1}{x}$ is the same function as the one you worked out $\endgroup$
    – Loobear23
    Apr 9, 2021 at 21:50

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