Describe the steps involved in finding the inverse of a function algebraically.

To find the inverse of a function algebraically, start by replacing the function notation \( f(x) \) with \( y \). Then, swap \( x \) and \( y \) to reflect that you're finding the inverse. After that, solve the resulting equation for \( y \) to express it in terms of \( x \). Finally, replace \( y \) with \( f^{-1}(x) \) to denote the inverse function. When you’re solving for \( y \), keep an eye out for common mistakes! One frequent hiccup is forgetting to switch the variables correctly, or neglecting to check that the function is one-to-one. Remember, only functions that pass the horizontal line test can have inverses. So, make sure to verify that your original function fulfills this criteria before getting too far along!