Find the value of the function for the given value of x. See Example 3. ƒ(x)=[[3-(x/2)]], for x=1

Verified step by step guidance

1. Identify the function and the value of x given in the problem. The function is ƒ(x) = [[3 - (x/2)]] and the value of x is 1.
2. Substitute the value of x into the function. Replace x with 1 in the expression 3 - (x/2).
3. Simplify the expression inside the brackets. Calculate the value of (1/2) and subtract it from 3.
4. Evaluate the expression to find the value of the function. After simplifying, determine the result of the expression inside the brackets.
5. Since the function includes double brackets, ensure to interpret or simplify it correctly based on the context or additional instructions provided (e.g., rounding, floor function, etc.).

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) = [3 - (x/2)] indicates that for any value of x, we can compute a specific output by substituting x into the expression. Understanding this notation is crucial for evaluating the function at a given value.

Substitution

Substitution is the process of replacing a variable in an expression with a specific value. In the context of the function f(x) = [3 - (x/2)], substituting x = 1 means replacing x in the expression with 1 to find the corresponding output. This step is essential for calculating the function's value at a particular input.

Order of Operations

The order of operations is a set of rules that dictates the sequence in which mathematical operations should be performed to ensure consistent results. Commonly remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), applying these rules correctly is vital when evaluating expressions like f(x) to avoid errors in calculations.