Question

Answer the following:

Find the range of the following function.

f(x) = [x] – x

Answer 1

f(x) = [x] – x = – {x}     ...[∵ x = [x] + {x}]

∵ 0 ≤ {x} < 1

∴ 0 ≥ – {x} > – 1

∴ – 1 < f(x) ≤ 0

∴ Range = (– 1, 0]