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

Verified step by step guidance

1. Identify the function and the input value. The function given is ƒ(x) = [[x/4]], and the input value is x = 7.
2. Substitute the value of x into the function. Replace x with 7 in the function, so it becomes ƒ(7) = [[7/4]].
3. Calculate the division inside the brackets. Divide 7 by 4 to get 1.75.
4. Apply the floor function. The floor function, denoted by double brackets [[ ]], rounds down to the nearest whole number. So, [[1.75]] becomes 1.
5. The value of the function ƒ(x) for x = 7 is 1.

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.