Probability density function (PDF)
A probability density function (PDF) is a mathematical function that describes the likelihood of a random variable taking on a specific value. In other words, it gives the probability of the random variable being within a certain range of values. The PDF is used to model continuous random variables, such as height or weight, where the variable can take on any value within a certain range.

Continuous function
A continuous function is a function that is defined for all real numbers within a certain range and has no breaks or gaps in its graph. In other words, it is a function that can take on any value within a certain interval. Examples of continuous functions include polynomials, exponential functions, and trigonometric functions.

Relationship between continuous function and PDF
When X is a continuous function, the function f(x) can be considered as a probability density function (PDF). This is because the PDF represents the probability of the random variable X taking on a specific value within a given interval.

Probability mass function (PMF)
On the other hand, a probability mass function (PMF) is used to model discrete random variables, where the variable can only take on specific values. The PMF gives the probability of the random variable taking on each of these specific values.

Explanation of the correct answer
In this question, since X is a continuous function, the function f(x) cannot be a probability mass function (PMF), as PMF is used for discrete random variables. Instead, f(x) can be considered as a probability density function (PDF) since it represents the probability of X taking on a specific value within a certain range.

Therefore, the correct answer is option 'B' - probability density function (PDF).