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

Question

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

Aicharya · Accepted Answer

Let $\mathrm{f}(x)=y \Rightarrow x=\mathrm{f}^{-1}(y)$ $\begin{aligned} & y=\frac{2 x-3}{3 x-4} \ & \Rightarrow 3 x y-4 y=2 x-3 \ & \Rightarrow x(3 y-2)=4 y-3 \ & \Rightarrow x=\frac{4 y-3}{3 y-2} \ & \Rightarrow \mathrm{f}^{-1}(y)=\frac{4 y-3}{3 y-2} \ & \Rightarrow \mathrm{f}^{-1}(x)=\frac{4 x-3}{3 x-2} \end{aligned}$

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

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