Question

(i) Let {x} & [x] denote the fractional and integral part of a real number x respectively. Solve 4{x} = x + [x]

(ii) Draw graph of f(x) = sgn (ln x)

Answer 1

(i) As x = [x] + {x}

∴ Given equation ⇒ 4{x} = [x] + {x} + [x] 

⇒ {x} = 2[x]/3

As [x] is always an integer and {x} ∈ [0, 1), possible values are

∴ There are two solution of given equation x = 0 and x = 5/3

(ii)