The Greatest and Least Integer Functions

For what values of x is

b. ⌈x⌉ = 0

검증된 단계별 안내

Understand the ceiling function ⌈x⌉, which rounds a number up to the nearest integer. For example, ⌈2.3⌉ = 3 and ⌈-1.7⌉ = -1.

To find the values of x for which ⌈x⌉ = 0, consider the definition: ⌈x⌉ is the smallest integer greater than or equal to x.

Since ⌈x⌉ = 0, x must be less than or equal to 0 but greater than -1, because ⌈x⌉ rounds up to the nearest integer.

Therefore, the values of x that satisfy ⌈x⌉ = 0 are those in the interval (-1, 0].

Express the solution in interval notation: x ∈ (-1, 0].

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

도움이 되었나요?

주요 개념

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

Greatest Integer Function (Ceiling Function)

The greatest integer function, denoted as ⌈x⌉, returns the smallest integer that is greater than or equal to x. For example, ⌈2.3⌉ equals 3, while ⌈-1.5⌉ equals -1. This function is crucial for understanding how to manipulate and solve equations involving integer constraints.

Understanding Zero in the Context of the Ceiling Function

To solve the equation ⌈x⌉ = 0, we need to determine the range of x values that yield a ceiling of zero. Since the ceiling function rounds up to the nearest integer, this means x must be in the interval [-1, 0). Thus, any value of x within this range will satisfy the equation.

Intervals and Inequalities

Understanding intervals and inequalities is essential for solving equations involving functions like the ceiling function. In this case, the solution involves identifying the interval where the function holds true, which is critical for determining valid x values that meet the specified condition.

The Greatest and Least Integer FunctionsFor what values of x isb. ⌈x⌉ = 0