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Chain Rule of Differentiation

Find f-1x i...

Question

Find $f^{- 1} (x)$ if $f (x) = \frac{x}{1 + x}$

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Solution

Let $y = f (x) ⟹ x = f^{- 1} (y)$
$y = \frac{x}{1 + x} y + x y = x y = x - x y y = (1 - y) x x = \frac{y}{1 - y} f^{- 1} (y) = \frac{y}{1 - y} f^{- 1} (x) = \frac{x}{1 - x}$

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