## Precalculus (6th Edition) Blitzer

The inverse of the function is ${{f}^{-1}}\left( x \right)=\frac{x+4}{3}$.
Let $f\left( x \right)=y$ This implies, $y=3x-4$. Now, by interchanging x and y, we get: $x=3y-4$ Solve for y. Add 4 to both sides in the above equation: \begin{align} & x+4=3y-4+4 \\ & x+4=3y \end{align} Now, divide the above equation by 3: $\frac{x+4}{3}=\frac{3y}{3}$ This gives: $y=\frac{x+4}{3}$. Replace y with ${{f}^{-1}}\left( x \right)$. Therefore, ${{f}^{-1}}\left( x \right)=\frac{x+4}{3}$ Therefore, the inverse of the function $f\left( x \right)=3x-4$ is $\frac{x+4}{3}$. .