Consider the function f in A = R − { 3 2 } defined as f ( x ) = 6 x − 4 4 x + 3 , then f − 1 is equal to

Given f ( x ) = 6 x − 4 4 x + 3 Let y = 6 x − 4 4 x + 3 , ⇒ 6 x y − 4 y = 4 x + 3 ⇒ x ( 6 y − 4 ) = 3 + 4 y ⇒ x = 6 y − 4 3 + 4 y f − 1 ( x ) = 6 x − 4 3 + 4 x

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MathematicsFunctionsInverseEasy2 minPYQ_2023

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Consider the function $f$ in $A = R - {\frac{2}{3}}$ defined as $f (x) = \frac{4 x + 3}{6 x - 4}$ , then $f^{- 1}$ is equal to

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Solution:

Given $f (x) = \frac{4 x + 3}{6 x - 4}$
Let $y = \frac{4 x + 3}{6 x - 4}$ ,
$\Rightarrow 6 x y - 4 y = 4 x + 3 \Rightarrow x (6 y - 4) = 3 + 4 y \Rightarrow x = \frac{3 + 4 y}{6 y - 4} f^{- 1} (x) = \frac{3 + 4 x}{6 x - 4}$

Stream:BITSATSubject:MathematicsTopic:FunctionsSubtopic:Inverse

⏱ 2mℹ️ Source: PYQ_2023

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