Please help with simplfying a floor/ceiling function

[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

 

[tacman]

The first step you have taken to simplify the expression is incorrect. In the original expression, the x value is being subtracted by 1/2 before it is passed into the ceiling function. This means that the value inside the ceiling function will always be equal to or greater than x-1/2. Therefore, when you remove the 1/2, you are changing the value inside the ceiling function and potentially changing the result of the expression.

To properly simplify the expression, you can first start by simplifying the ceiling function. Remember that the ceiling function rounds up to the nearest integer. So, Ceiling[x-1/2] would be equal to x if x is a whole number, or x+1 if x is a decimal.

Next, you can simplify the floor function by applying the same logic. Floor[x-1/2-7/5] would be equal to x-2 if x is a whole number, or x-1 if x is a decimal.

Therefore, the simplified expression would be Floor[Ceiling[x]-2] if x is a whole number, or Floor[Ceiling[x]-1] if x is a decimal.

I hope this helps and good luck on your test tomorrow! Remember to always double check your work and make sure you properly understand the concepts before applying them.