Answer
The inverse of the function is ${{f}^{-1}}\left( x \right)=\frac{x+4}{3}$.
Work Step by Step
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 $\frac{x+4}{3}$.
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