Composition of Functions

[peteski]

I need some help with this question:

Let f, g : R -> Z be the floor and ceiling functions, respectively. Compute f o g(x) and g o f(x).

Thank you!

 

[pka]

I need some help with this question:

Let f, g : R -> Z be the floor and ceiling functions, respectively. Compute f o g(x) and g o f(x).

If \(\displaystyle x \in Z\) then \(\displaystyle \left\lceil x \right\rceil = x\,\& \,\left\lfloor x \right\rfloor = x\).

 

[Ishuda]

I need some help with this question:

Let f, g : R -> Z be the floor and ceiling functions, respectively. Compute f o g(x) and g o f(x).

Thank you!

For any x \(\displaystyle \epsilon\) R
x = z + t; 0\(\displaystyle \le\) t < 1
and z \(\displaystyle \epsilon\) Z. If t=0 then f(x) = g(x) = f o g(x) = g o f(x) = z. If t is not zero, then ...