The greatest integer function, denoted by [x], returns the largest integer less than or equal to x. This function is discontinuous at integer values and continuous at non-integer values.
Let's analyze the given options:
(A) x = 1: This is an integer. The function is discontinuous at x = 1.
(B) x = 1.5: This is not an integer. The function is continuous at x = 1.5.
(C) x = -2: This is an integer. The function is discontinuous at x = -2.
(D) x = 4: This is an integer. The function is discontinuous at x = 4.
Therefore, the function f(x) = [x] is continuous at x = 1.5.
Correct Answer: x=1.5
AI Suggestion: Option B
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Pedagogical Audit
Bloom's Analysis:
This is an UNDERSTAND question because the student needs to comprehend the properties of the greatest integer function and its continuity.
Knowledge Dimension:CONCEPTUAL
Justification:The question requires understanding the concept of continuity and the properties of the greatest integer function, rather than just recalling facts or applying a specific procedure.
Syllabus Audit:
In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly tests the knowledge of continuity of functions, specifically the greatest integer function, which is a standard topic in the syllabus.