If $f(x) = \frac{x}{{1 + x}}$, then ${f^{ - 1}}(x)$ is equal to

  • A

    $\frac{{(1 + x)}}{x}$

  • B

    $\frac{1}{{(1 + x)}}$

  • C

    $\frac{{(1 + x)}}{{(1 - x)}}$

  • D

    $\frac{x}{{(1 - x)}}$

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