Fractional Part Function

What is a Fractional Part Function in Math?

The Fractional Part Function, denoted as {x} or frac(x), in mathematics, extracts the decimal part of a real number x. It represents the fractional component of x after the decimal point, excluding the integer part.

What is Range of Fractional Part Function?

The range of the Fractional Part Function is the interval [0, 1), meaning it includes 0 (inclusive) but excludes 1. The function produces decimal values between 0 and 1, showcasing its periodic nature.

What is Derivative of Fractional Part Function?

The Fractional Part Function is not differentiable at integer points due to its step-like behavior. Therefore, the derivative is undefined at these points. However, the derivative exists elsewhere and equals 0 for non-integer values.

Is Fractional Part Function Continuous?

The Fractional Part Function is discontinuous at integer values, where abrupt changes occur in its value. While exhibiting discontinuities, it is continuous in the intervals between integers.

What is Domain of Fractional Part of x?

The domain of the Fractional Part Function encompasses all real numbers. It is applicable to any real value of x, denoted as R or (-∞, ∞).

Is Fractional Part Function Periodic?

Yes, the Fractional Part Function is periodic with a period of 1. The pattern of the function repeats every interval of 1 along the x-axis. This periodicity is evident in its step-like graph and the fact that {x+1}={x} for any real number x.

Fractional Part Function, often denoted as {x}, represents the decimal part of a real number x after removing its integer part. In simpler terms, it captures the fractional portion of a number, excluding the whole number component. The fractional part function is particularly useful in various mathematical contexts, such as number theory, analysis, and computer science, where understanding the non-integer portion of a number is essential.

In this article, we will learn about the various concepts related to the fractional part function, like the meaning and definition of the fractional part function, properties of the fractional part function, its formula, application, graph, and solved examples for better understanding.