Answer
\[\left( {{f}^{-1}} \right)'\left( x \right)=\frac{1}{3}\]
Work Step by Step
\[\begin{align}
& f\left( x \right)=3x-4 \\
& \text{Write }f\left( x \right)\text{ as }y \\
& y=3x-4 \\
& \text{Interchange }x\text{ and }y \\
& x=3y-4 \\
& \text{Solve for }y \\
& 3y=x+4 \\
& y=\frac{1}{3}x+\frac{4}{3} \\
& \text{Write }y\text{ as }{{f}^{-1}}\left( x \right) \\
& {{f}^{-1}}\left( x \right)=\frac{1}{3}x+\frac{4}{3} \\
& \text{Compute the derivative} \\
& \left( {{f}^{-1}} \right)'\left( x \right)=\frac{d}{dx}\left[ \frac{1}{3}x+\frac{4}{3} \right] \\
& \left( {{f}^{-1}} \right)'\left( x \right)=\frac{1}{3} \\
\end{align}\]
