Q87 / 150 · MHT CET 2023 (14 May Shift 2) · Mathematics

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

  • Correct answer
    A
    $\frac{4 x-3}{3 x-2}$
  • B
    $\frac{3 x-2}{4 x+3}$
  • C
    $\frac{3 x-4}{4 x-2}$
  • D
    $\frac{2 x+3}{4 x-3}$

Solution

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

Hence, the correct answer is option: 'A'.

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