Question

Show that $f:R\to R$ given by $f\left(x\right)=3x-4$ is one-one and onto. Find its inverse function.
Also, find $f^{-1}\left(9\right)$ and $f^{-1}(-2)$.

Answer 1

$f\left(x\right)=3x-4y=3x-4\therefore y+4=3x\therefore x=\left(\frac{y+4}{3}\right)or{f}^{-1}\left(y\right)=\left(\frac{y+4}{3}\right)so{f}^{-1}x=\left(\frac{x+4}{3}\right)andthen{f}^{-1}\left(9\right)=\left(\frac{9+4}{3}\right)=\left(\frac{13}{3}\right)f^{-1}(-2)=\left(\frac{-2+4}{3}\right)=\left(\frac{2}{3}\right)$