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

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1.Relation and Function

easy

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

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

Solution

(d) $f(x) = \frac{x}{{1 + x}}$. Let $y = f(x) \Rightarrow x = {f^{ – 1}}(y)$

$\therefore$ $y = \frac{x}{{1 + x}} \Rightarrow y + yx = x$

==> $x = \frac{y}{{1 – y}}$

==> ${f^{ – 1}}(y) = \frac{y}{{1 – y}}$

==> ${f^{ – 1}}(x) = \frac{x}{{1 – x}}$.

Standard 12

Mathematics

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