Let f : R − {−1} → R − {1} be given by\[f\left( x \right) = \frac{x}{x + 1} . \text{Write } f^{- 1} \left( x \right)\]

\[Let f^{- 1} \left( x \right) = y . . . \left( 1 \right)\] \[ \Rightarrow f\left( y \right) = x\] \[ \Rightarrow \frac{y}{y + 1} = x\] \[ \Rightarrow y = xy + x\] \[ \Rightarrow y - xy = x\] \[ \Rightarrow y\left( 1 - x \right) = x\] \[ \Rightarrow y = \frac{x}{1 - x}\] \[ \Rightarrow f^{- 1} \left( x \right) = \frac{x}{1 - x} [\text{from}\left( 1 \right)]\]

Let F : R − {−1} → R − {1} Be Given by - Mathematics

प्रश्न

Let f : R − {−1} → R − {1} be given by $f (x) = \frac{x}{x + 1} . Write f^{- 1} (x)$

उत्तर

$L e t f^{- 1} (x) = y . . . (1)$
$\Rightarrow f (y) = x$
$\Rightarrow \frac{y}{y + 1} = x$
$\Rightarrow y = x y + x$
$\Rightarrow y - x y = x$
$\Rightarrow y (1 - x) = x$
$\Rightarrow y = \frac{x}{1 - x}$
$\Rightarrow f^{- 1} (x) = \frac{x}{1 - x} [from (1)]$

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Types of Functions

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पाठ 2: Functions - Exercise 2.5 [पृष्ठ ७३]

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पाठ 2 Functions
Exercise 2.5 | Q 22 | पृष्ठ ७३

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Let F : R − {−1} → R − {1} Be Given by - Mathematics

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