The equation f(x₀) = x₀ describes a function where the output is equal to the input. This means that when you plug a specific value x₀ into the function f , the result is the same value x₀ . Such functions are known as identity functions, which can be represented as f(x) = x . In this context, x₀ can be any number, and the function f simply returns that number. Identity functions are important in mathematics because they serve as a baseline for understanding other types of functions and transformations, such as linear functions and polynomial functions.