Question
Download Solution PDFLet z = [y] and y = [x] - x, where [.] is the greatest integer function. If x is not an integer but positive, then what is the value of z?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
Since, {x}+[x] = x
⇒x – [x] = {x}
⇒ 0≤ x – [x] < 1 (0 ≤ {x} < 1)
⇒ –1 ≤ [x] –x ≤ 0
But x is positive and non-integer; then
⇒ –1 < [x]–x < 0
⇒ –1 < y < 0
⇒ [y] = –1
∴ Option (a) is correct.
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