Final Answer:
f(x) represents a function in mathematics. Therefore the correct option is b. Inverse of a function.
Step-by-step explanation:
In mathematics, a function is represented by the symbol f, followed by parentheses containing the variable x, such as f(x). This notation signifies that the output of the function (represented by f(x)) is dependent on the input variable x. The concept of an inverse function is denoted by f^(-1)(x), where the inverse undoes the operation of the original function. In other words, if y = f(x), then x = f^(-1)(y).
The inverse function reverses the roles of the input and output, swapping x and y. This is essential because it allows us to find the original input value when given the output value of a function. In the context of the provided options, option b accurately describes the nature of f(x) as the inverse of a function. Therefore, f(x) is not the exponent of -1 (option a) or the reciprocal of f(x) (option c).
Understanding the representation of functions and their inverses is fundamental in mathematics, as it enables the analysis and manipulation of relationships between variables. In real-world applications, the concept of inverse functions is crucial for problem-solving and modeling various phenomena where one variable depends on another.