Find the value of the function for the given value of x. See Example 3. ƒ(x)=[[x]], for x=-√2

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 greatest integer function, denoted as [[x]], returns the largest integer less than or equal to x. This concept is essential for solving the problem, as it requires determining the integer part of the input value, which can significantly affect the output of the function.

Evaluating Functions

Evaluating a function involves substituting a specific value into the function's expression to find the corresponding output. In this case, substituting x = -√2 into the greatest integer function requires understanding how to handle irrational numbers and their relationship to integers.