If f(x) = frac{2x - 3}{3x - 4},x neq frac{4}{ | vedclass

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Question

(A) Let $f(x) = y$,which implies $x = f^{-1}(y)$.Given $y = \frac{2x - 3}{3x - 4}$.Multiply both sides by $(3x - 4)$:$y(3x - 4) = 2x - 3$$3xy - 4y = 2

Vedclass · Accepted Answer

$\frac{4x - 3}{3x - 2}$

Vedclass · Answer

(A) Let $f(x) = y$,which implies $x = f^{-1}(y)$.Given $y = \frac{2x - 3}{3x - 4}$.Multiply both sides by $(3x - 4)$:$y(3x - 4) = 2x - 3$$3xy - 4y = 2x - 3$Rearrange the terms to isolate $x$:$3xy - 2x = 4y - 3$$x(3y - 2) = 4y - 3$$x = \frac{4y - 3}{3y - 2}$Since $x = f^{-1}(y)$,we have $f^{-1}(y) = \frac{4y - 3}{3y - 2}$.Replacing $y$ with $x$,we get $f^{-1}(x) = \frac{4x - 3}{3x - 2}$.

If $f(x) = \frac{2x - 3}{3x - 4}$,$x \neq \frac{4}{3}$,then the value of $f^{-1}(x)$ is

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