To find the inverse of a function, you typically follow these steps:

1. Replace the function notation $f(x)$ with $y$.
2. Swap $x$ and $y$ in the equation.
3. Solve for $y$, which represents the inverse function $f^{-1}(x)$.

Let’s go through an example. Suppose you have the function:

$f(x) = -8x + 2$

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

$y = -8x + 2$

Step 2: Swap $x$ and $y$:

$x = -8y + 2$

Step 3: Solve for $y$:

$x - 2 = -8y$ $y = \frac{2 - x}{8}$

So, the inverse function is: $f^{-1}(x) = \frac{2 - x}{8}$

Would you like to explore more about inverse functions, or do you have any questions?

Related Questions:

1. How would you find the inverse of $f(x) = 3x - 7$?
2. What is the graphical interpretation of a function and its inverse?
3. Can all functions have an inverse? Why or why not?
4. How do you verify that two functions are inverses of each other?
5. What is the inverse of the function $f(x) = \frac{1}{x}$?

Tip: To check if a function and its inverse are correct, compose them (i.e., $f(f^{-1}(x))$ and $f^{-1}(f(x))$) and see if you get $x$ in both cases.