Find the value of the function for the given value of x. 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 \( x = 1 \).
2. Substitute the value of \( x = 1 \) 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. Evaluate the floor function \( \left\lfloor \cdot \right\rfloor \), which means finding the greatest integer less than or equal to the simplified value.
5. Write the final expression for \( f(1) \) after applying the floor function, which gives the value of the function at \( x = 1 \).

Key Concepts

Function Evaluation

Function evaluation involves substituting a given input value into the function's expression and simplifying to find the output. For example, if ƒ(x) = 3 - (x/2), to find ƒ(1), replace x with 1 and simplify the expression.

Order of Operations

The order of operations dictates the sequence in which mathematical operations are performed: parentheses, exponents, multiplication and division (left to right), then addition and subtraction (left to right). Correctly applying this ensures accurate simplification of expressions.

Floor Function (Greatest Integer Function)

The floor function, denoted by [[x]], returns the greatest integer less than or equal to x. For example, [[2.7]] = 2 and [[-1.3]] = -2. Understanding this helps interpret the function ƒ(x) = [[3 - (x/2)]] correctly.