Relations and Functions Question - CBSE

Question

Let $f: \mathbb{R} \setminus \{-4/3\} o \mathbb{R}$ be a function defined as $f(x) = \dfrac{4x}{3x+4}$. The inverse of $f$ is the map $g: ext{Range } f o \mathbb{R} \setminus \{-4/3\}$ 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

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

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🎯 Official CBSE Marking Scheme:
Evaluating inverse function $g(y) = \frac{4y}{4-3y}$: 1.0 Mark

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