Mark (√) against the correct answer in the following:

Question:

Mark (√) against the correct answer in the following:

Let $\mathrm{f}: \mathrm{R}-\left\{\frac{-4}{3}\right\} \rightarrow-\left\{\frac{4}{3}\right\}: \mathrm{f}(\mathrm{x})=\frac{4 \mathrm{x}}{(3 \mathrm{x}+4)}$. Then $\mathrm{f}^{-1}(\mathrm{y})=$ ?

A. $\frac{4 y}{(4-3 y)}$

B. $\frac{4 y}{(4 y+3)}$

C. $\frac{4 y}{(3 y-4)}$

D. None of these 

Solution:

$f(x)=\frac{4 x}{3 x+4}$

$\Rightarrow y=\frac{4 x}{3 x+4}$

$x \Longleftrightarrow y$

$\Rightarrow \mathrm{x}=\frac{4 y}{3 y+4}$

$\Rightarrow 3 y x+4 x=4 y$

$\Rightarrow y(3 x-4)=-4 x$

$\Rightarrow y=\frac{4 x}{4-3 x}$

$x \Longleftrightarrow y$

$\Rightarrow \mathrm{X}=\frac{4 y}{4-3 y}$

 

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