If f(x)f(x) is odd then is g(x)=⌊f(x)⌋g(x)=⌊f(x)⌋ also odd?

Answer 1

floor( -3.25) = -4 <--- the greatest integer less than -3.25

floor( 3.25) = 3

So does floor(-3.25) = - floor(3.25)?

Answer 2

Given f(x) as odd function: f(-x)= - f(x)

g(-x) = ⌊f(-x)⌋=⌊-f(x)⌋ != -⌊f(x)⌋ since floor function ⌊z⌋ yields the nearest integer smaller than z

For example when z=3.5, ⌊3.5⌋ = 3 while when z=-3.5, ⌊-3.5⌋ = -4

Therefore g(-x) != -g(x) so g(x) is not an odd function