Question

If $f:R-\{-\frac{4}{3}\}\to R$ be a function defined by $f\left(x\right)=\frac{4x}{3x+4}$ Show that the function $f$ is invertible, Also find the inverse of $f$

Answer 1

$\begin{array}{c}f\left(x\right)=\frac{4x}{3x+4}\\ Letf\left(x\right)=y\\ \Rightarrow y=\frac{4x}{3x+4}\\ \Rightarrow 3xy+4y-4x=0\\ \Rightarrow x\left(3y-4\right)+4y=0\\ \Rightarrow x=\frac{-4y}{\left(3y-4\right)}\\ \therefore f^{-1}\left(x\right)=\frac{4x}{\left(4-3x\right)}\end{array}$