Find the value of the function for the given value of x. ƒ(x)=[[x/4]], for x=7

Verified step by step guidance

1. Identify the function given: \( f(x) = \left\lfloor \frac{x}{4} \right\rfloor \), where \( \left\lfloor \cdot \right\rfloor \) denotes the floor function, which means rounding down to the nearest integer.
2. Substitute the given value \( x = 7 \) into the function: \( f(7) = \left\lfloor \frac{7}{4} \right\rfloor \).
3. Calculate the division inside the floor function: \( \frac{7}{4} \).
4. Apply the floor function to the result of the division, which means take the greatest integer less than or equal to \( \frac{7}{4} \).
5. Write the final expression for \( f(7) \) as the floor of \( \frac{7}{4} \) and interpret the value accordingly.

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.

Floor Function (Greatest Integer Function)

The floor function, denoted by [[x]], returns the greatest integer less than or equal to x. For example, [[3.7]] = 3 and [[-1.2]] = -2. It essentially 'rounds down' to the nearest whole number.

Order of Operations

When evaluating expressions, follow the order of operations: parentheses, exponents, multiplication and division (left to right), then addition and subtraction (left to right). This ensures correct simplification before applying the floor function.