Find the value of the function for the given value of x. See Example 3. ƒ(x)=[[x]], for x=x-(-π)

Key Concepts

Function Notation

Function notation, such as ƒ(x), represents a mathematical relationship where each input x corresponds to exactly one output. Understanding this notation is crucial for evaluating functions, as it indicates how to compute the output based on the given input value.

Greatest Integer Function

The notation [[x]] typically denotes the greatest integer function, also known as the floor function. This function rounds down a real number x to the nearest integer less than or equal to x. For example, [[3.7]] equals 3, while [[-2.3]] equals -3.

Algebraic Manipulation

Algebraic manipulation involves rearranging and simplifying expressions to solve equations or evaluate functions. In this context, understanding how to manipulate the expression x = x - (-π) is essential for determining the correct value of x to substitute into the function.