To find the inverse of the function $f(x) = 8x - 9$, denoted as $f^{-1}(x)$, follow these steps:

Step 1: Replace $f(x)$ with $y$.

$y = 8x - 9$

Step 2: Solve for $x$ in terms of $y$.

$y = 8x - 9$ Add 9 to both sides: $y + 9 = 8x$ Now, divide both sides by 8: $x = \frac{y + 9}{8}$

Step 3: Replace $y$ with $x$ to express the inverse function.

$f^{-1}(x) = \frac{x + 9}{8}$

Thus, the inverse function is: $f^{-1}(x) = \frac{x + 9}{8}$

Would you like further details or have any questions?

Here are 5 related questions you might find useful:

1. How can we verify that $f(f^{-1}(x)) = x$?
2. What is the domain and range of $f(x) = 8x - 9$?
3. How do you find the inverse of a quadratic function?
4. What does the inverse function tell us about the original function?
5. How do transformations affect the graph of $f(x)$ and its inverse?

Tip: When finding the inverse, always switch $x$ and $y$ and then solve for $y$.