(a) Find the inverse function of $f(x)=7 x-6$.
\[
f^{-1}(x)=
\]
(b) The graphs of $f$ and $f^{-1}$ are symmetric with respect to the line defined by $y=$
Answer
Final Answer: The inverse function of \(f(x)=7x-6\) is \(f^{-1}(x)=\boxed{\frac{x}{7}+\frac{6}{7}}\).
Step 1 ：The inverse function of a function can be found by swapping the x and y values and solving for y. In this case, we need to find the inverse of \(f(x)=7x-6\). This means we need to solve the equation \(x=7y-6\) for y.
Step 2 ：Solving the equation \(x=7y-6\) for y, we get \(y=\frac{x}{7}+\frac{6}{7}\).
Step 3 ：So, the inverse function of \(f(x)=7x-6\) is \(f^{-1}(x)=\frac{x}{7}+\frac{6}{7}\).
Step 4 ：Final Answer: The inverse function of \(f(x)=7x-6\) is \(f^{-1}(x)=\boxed{\frac{x}{7}+\frac{6}{7}}\).
