Question

Solve for x, where [ . ] represents greatest integer function and {.} represent fractional part function.

(i) |[x] - 2x| = 4 

(ii) [x – 1] + [1 – x] + x – {x} > 0 

Answer 1

(i) [x] – 2x = ± 4 take two cases x ∈ I & x ∉ I

[x] – 2x = ±4

Case-I : x ∈ I

x – 2x = ±4 

⇒ x = {–4, 4}