What is the first step in finding the inverse of a function?

The first step in finding the inverse of a function is to switch x and y. This process involves taking the original function, which is typically expressed in the form y = f(x), and rewriting it as x = f(y). This switch is foundational because the goal of finding an inverse function is to express y in terms of x, essentially reversing the roles of the input and output.

By switching the variables, you set the stage to solve for y, leading to the formulation of the inverse function. This step is crucial because it captures the relationship between the two variables, allowing for the necessary manipulations and algebraic steps to isolate y and express it correctly as a function of x.

Other options may be relevant in the broader context of working with functions and their inverses, but they do not serve as the first step in finding an inverse. For example, calculating the derivative relates to understanding the function's behavior but is not central to the inverse process. Similarly, graphing the function can help visualize the relationship and check if the function is one-to-one, while identifying the function's domain is important for understanding the range of the inverse but does not precede the switching step.