Find the value of the function for the given value of x. See Example 3. ƒ(x)=[[0.5x]], 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) = [[0.5x]] indicates that the function takes the value of x, applies the operation 0.5x, and then applies the floor function, denoted by [[ ]], which rounds down to the nearest integer.

Floor Function

The floor function, denoted as [[x]], is a mathematical function that returns the greatest integer less than or equal to x. For example, [[3.7]] equals 3, and [[-2.3]] equals -3. Understanding how the floor function operates is crucial for accurately determining the output of f(x) when evaluating specific values of x.

Evaluating Functions

Evaluating a function involves substituting a specific value for the variable and performing the necessary calculations to find the output. In this case, to find f(7), you would substitute 7 into the function f(x) = [[0.5x]], calculate 0.5 * 7, and then apply the floor function to the result to obtain the final value.