Question

Interval in which {x} is monotonically increasing function, where { } is fractional part function -

• A. $[0,1)$
• B. $[\frac{1}{2},\frac{3}{2}]$
• C. $[1,2)$
• D. $[\frac{3}{2},\frac{5}{2}]$

Answer 1

Answer: (A), (C)

$[1,2)$

When we look at the graph of fractional part function, it goes from [0, 1) in the interval

[I , I+1), where I is an integer. Thus it behaves as a monotonic function in the interval [I , I+1).

Hence, [0,1) & [1,2) and all other intervals like these are the intervals where {x} is monotonically increasing function.