Find the value of the function for the given value of x. See Example 3. ƒ(x)=[[0.5x]], for x=7

Verified step by step guidance

1. Identify the function and the value of x given in the problem. Here, the function is ƒ(x) = [[0.5x]] and x = 7.
2. Substitute the value of x into the function. Replace x with 7 in the function, so it becomes ƒ(7) = [[0.5 * 7]].
3. Calculate the product inside the brackets. Multiply 0.5 by 7.
4. Evaluate the double brackets. The double brackets typically indicate the floor function, which rounds down to the nearest integer.
5. Write down the expression with the floor function applied to the result from step 3.

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.