Answer
The inverse function, ${{f}^{-1}}\left( x \right)$ for $f\left( x \right)=7x-1$ is $\frac{x}{7}+\frac{1}{7}$.
Work Step by Step
Consider the provided function,
$f\left( x \right)=7x-1$
Follow the steps to find an inverse of the function to get the inverse of $f\left( x \right)=7x-1$.
Step 1: Replace $f\left( x \right)$ with $y$.
$y=7x-1$
Step 2: Interchange $y$ and $x$.
$x=7y-1$
Step 3: Solve for $y$.
$\begin{align}
& x=7y-1 \\
& x+1=7y-1+1 \\
& x+1=7y \\
& \frac{x+1}{7}=y
\end{align}$
Step 4: Replace $y$ with ${{f}^{-1}}\left( x \right)$.
${{f}^{-1}}\left( x \right)=\frac{x+1}{7}$
Thus, the inverse function for $f\left( x \right)=7x-1$ is ${{f}^{-1}}\left( x \right)=\frac{x}{7}+\frac{1}{7}$.
