11. b. [ x-4 /3 ]=x+1 /2 ,dar stim din proprietatile partii intregi a unui numar x∈R faptul ca [x]∈Z => [ x-4 /3 ]=k ,unde k∈Z <=> x+1 /2=k <=> x=2k-1 .
k <= x-4 /3 < k+1 <=> k <= 2k-5 /3 < k+1 <=> 3k <= 2k-5 < 3k+3 <=> 0 <= -k-5 < 3 => 0 <= -k-5 => 5 <= -k <=> k < = -5 si -k-5 < 3 => -k < 8 => k > -8 dar deoarece k∈Z => k∈{-7;-6;-5} => x∈{-15;-13;-11} . Analog se face si a) .
