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 given function and the value of \( x \). The function is \( f(x) = \left\lfloor 3 - \frac{x}{2} \right\rfloor \), and we need to find \( f(1) \).
2. Substitute \( x = 1 \) into the function: \( f(1) = \left\lfloor 3 - \frac{1}{2} \right\rfloor \).
3. Simplify the expression inside the floor function: calculate \( 3 - \frac{1}{2} \).
4. Understand that the floor function \( \left\lfloor y \right\rfloor \) means taking the greatest integer less than or equal to \( y \).
5. Apply the floor function to the simplified value from step 3 to find \( f(1) \).

Key Concepts

Function Notation and Evaluation

Function notation, written as ƒ(x), represents a rule that assigns each input x to exactly one output. Evaluating a function means substituting the given value of x into the function's expression and simplifying to find the output.

Order of Operations

The order of operations dictates the sequence in which mathematical operations are performed: parentheses first, then exponents, followed by multiplication and division (left to right), and finally addition and subtraction (left to right). This ensures consistent and correct evaluation of expressions.

Floor Function

The floor function, denoted by double brackets [[ ]], rounds a real number down to the greatest integer less than or equal to that number. For example, [[3.7]] = 3 and [[-1.2]] = -2. It is important to apply this after evaluating the expression inside.