The equation f^-1(y) = x represents the inverse function of f . In this context, f is a function that takes an input x and produces an output y . The inverse function, denoted as f^-1 , reverses this process, meaning it takes y as input and returns the original x . For example, if f(x) = y means that when you input x , you get y , then f^-1(y) = x indicates that if you start with y , you can find back the original x . This relationship is crucial in mathematics, particularly in solving equations and understanding function behavior.