Relations and Functions Question - CBSE

Question

Let $f: \mathbb{R} - \{-4/3\} ightarrow \mathbb{R}$ be a function defined as $f(x) = \dfrac{4x}{3x + 4}$. The inverse of $f$ is the map $g: ext{Range } f ightarrow \mathbb{R} - \{-4/3\}$ given by:
(a) $g(y) = \dfrac{4y}{4 - 3y}$
(b) $g(y) = \dfrac{3y}{4 - 3y}$
(c) $g(y) = \dfrac{4y}{3 - 4y}$
(d) $g(y) = \dfrac{3y}{3 - 4y}$

Accepted Answer

$y(3x + 4) = 4x \Rightarrow x(4 - 3y) = 4y \Rightarrow x = \dfrac{4y}{4 - 3y}$. [1.0 Mark]

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🎯 Official CBSE Marking Scheme:
Solving inverse function $g(y) = 4y/(4-3y)$: 1.0 Mark

Question:

Step-by-Step Solution

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