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  4. Consider the function f in A=R- (2/3) defined as f (x)=(4x+3/6x-4). Find f-1.

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Q. Consider the function $f$ in $A=R-\left\{\frac{2}{3}\right\}$ defined as $f \left(x\right)=\frac{4x+3}{6x-4}$. Find $f^{-1}$.

Relations and Functions - Part 2

Solution:

Let $y=\frac{4x+3}{6x-4}$
$\Rightarrow 6xy-4y=4x+3$
$\Rightarrow x=\frac{3+4y}{6y-4}$
$\therefore f ^{-1}\left(x\right)=\frac{3+4x}{6x-4}$