Question

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

• A. $\frac{3+4x}{6x-4}$
• B. $\frac{6x-4}{3+4x}$
• C. $\frac{3-4x}{6x-4}$
• D. $\frac{9+2x}{6x-4}$

Answer 1

Answer: (A)

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