Find the value of the function for the given value of x. See Example 3. ƒ(x)=[[x/4]], for x=7

Key Concepts

Function Notation

Function notation, such as f(x), represents a relationship where each input x corresponds to exactly one output. In this case, f(x) = [[x/4]] indicates that we are applying a specific operation to x, which is crucial for evaluating the function at a given value.

Greatest Integer Function

The notation [[x]] refers to the greatest integer function, also known as the floor function. It rounds down the value of x to the nearest integer. For example, [[3.7]] equals 3, and [[-2.3]] equals -3, which is essential for determining the output of f(x) in this problem.

Substitution

Substitution is the process of replacing a variable in a function with a specific value to evaluate the function. In this question, we substitute x = 7 into the function f(x) = [[x/4]] to find the corresponding output, which is a fundamental step in solving function-related problems.