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

검증된 단계별 안내

Identify the function given: \( f(x) = \lfloor 0.5x \rfloor \), where \( \lfloor \cdot \rfloor \) denotes the floor function, which means rounding down to the nearest integer.

Substitute the given value \( x = 7 \) into the function: \( f(7) = \lfloor 0.5 \times 7 \rfloor \).

Calculate the product inside the floor function: \( 0.5 \times 7 = 3.5 \).

Apply the floor function to \( 3.5 \), which means finding the greatest integer less than or equal to \( 3.5 \).

The result of the floor function is the value of \( f(7) \).

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Function Notation

Function notation, written as ƒ(x), represents a rule that assigns each input x to exactly one output. Understanding this notation helps interpret the problem as finding the output value when a specific input is given.

Floor Function

The floor function, denoted by [[x]], returns the greatest integer less than or equal to x. It essentially rounds down any decimal or fractional value to the nearest whole number below or equal to it.

Evaluating Functions at a Given Input

Evaluating a function at a given input means substituting the input value into the function's expression and simplifying. This process involves performing arithmetic operations and applying any special functions, like the floor function, to find the output.