Q49 / 100 · BITSAT 2023 (Memory Based Paper 2) · Mathematics
Consider the function $\mathrm{f}$ in $\mathrm{A}=\mathrm{R}-\left\{\frac{2}{3}\right\}$ defined as $f(x)=\frac{4 x+3}{6 x-4}$, then $f^{-1}$ is equal to
- Correct answerA$\frac{3+4 x}{6 x-4}$
- B$\frac{6 x-4}{3+4 x}$
- C$\frac{3-4 x}{6 x-4}$
- D$\frac{9+2 x}{6 x-4}$
Solution
Given $f(x)=\frac{4 x+3}{6 x-4}$
Let $y=\frac{4 x+3}{6 x-4}$,
$\begin{aligned}<br />& \Rightarrow 6 x y-4 y=4 x+3 \Rightarrow x(6 y-4)=3+4 y \\<br />& \Rightarrow x=\frac{3+4 y}{6 y-4} \\<br />& f^{-1}(x)=\frac{3+4 x}{6 x-4}<br />\end{aligned}$
Let $y=\frac{4 x+3}{6 x-4}$,
$\begin{aligned}<br />& \Rightarrow 6 x y-4 y=4 x+3 \Rightarrow x(6 y-4)=3+4 y \\<br />& \Rightarrow x=\frac{3+4 y}{6 y-4} \\<br />& f^{-1}(x)=\frac{3+4 x}{6 x-4}<br />\end{aligned}$
Hence, the correct answer is option: 'A'.