Find the value of the function for the given value of x. ƒ(x)=2-[[-x]], for x=3.7

검증된 단계별 안내

Identify the given function and the value of \( x \). The function is \( f(x) = 2 - \lfloor -x \rfloor \) and \( x = 3.7 \).

Substitute \( x = 3.7 \) into the function to get \( f(3.7) = 2 - \lfloor -3.7 \rfloor \).

Evaluate the expression inside the floor function: calculate \( -3.7 \).

Find the floor value \( \lfloor -3.7 \rfloor \), which is the greatest integer less than or equal to \( -3.7 \).

Subtract the floor value from 2 to find \( f(3.7) = 2 - \lfloor -3.7 \rfloor \).

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주요 개념

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

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 x-value into the function's expression and simplifying to find the output.

Floor Function (Greatest Integer Function)

The floor function, denoted by [[x]] or ⌊x⌋, returns the greatest integer less than or equal to x. For example, ⌊3.7⌋ = 3 and ⌊-2.3⌋ = -3. It is essential to understand how to apply this function when it appears inside expressions.

Order of Operations and Handling Negative Inputs

When evaluating expressions, follow the order of operations (PEMDAS). For the floor function applied to a negative value, carefully compute the inner value first (e.g., -x), then apply the floor function. This ensures accurate evaluation of the function.