Simplifying floor and ceiling function composition

[stunner5000pt]

note; This is NOT a homework assignment please help me because i need to know this properly for a test i have tomorrow

Given is a question Floor[ Ceiling [x-1/2] - 7/5 ] and they ask to graph it.

i'm fine with graphing it but simplfying this i what I'm a bit confused on

my first step was Floor [ Ceiling [ x ] - 1/2 - 7/5 ] and there's a mistake in the way i removed the 1/2 why?

please help

 

[matt grime]

because floor{x-y] does not equal floor[x] - y for a start? floor is not linear like that. replace the word lfoor there with ceiling.


simplify it? ok, ceiling is an integer valued function, so if i take off 7/5 from an integer and then take the floor of that, that's the same as taking off the other 3/5 isn't it? so it simplifies to ceiling[x-1/2] - 2