Answer
a) f (S) = {0, 1,3}.
b)f (S) = {0, 1,3}.
c)f(S) = {0,8, 16,40}.
d)f(S)= {1,12,33,65}
Work Step by Step
In each case, we need to compute the values of f(x) for each x ES.
a) Note that f(±2) =⌊ (±2)^2/3 ⌋ =⌊4/3⌋ = 1, f(±1) = ⌊ (±1)^2/3⌋ =⌊1/3⌋ = 0, f(0) = ⌊0^2/3⌋ = ⌊0⌋ = 0, and f (3) = ⌊3^2 /3 ⌋ = ⌊3⌋ = 3.
Therefore f (S) = {0, 1,3}.
b) In addition to the values we computed above, we can see that f(4) = 5 and f(5) = 8.
Therefore f(S) = {0,1,3,5,8}.
c)In the similar way as above Note this time also that f(7) = 16 and f(11) = 40, so
f(S) = {0,8, 16,40}.
d)f(S)= { f(2),f(6),f(10),f(14) } = {1,12,33,65}
