The domain of the given step function is:
The set of all the real numbers.
Ceiling function--
The ceiling function also known as the least integer function is the function which takes the largest value of the integer for a non-integer number which lie between the two integers , and gives the integer itself if the number is integer.
and it is given by:
[tex]f(x)=\left \lceil x \right \rceil[/tex]
(
For example--
if x= 0.5
then f(x)=1 since x lie between 0 and 1
if x= -2.5
Then f(x)= -2
since x lie between -3 and -2.
if x=3
then f(x)=3 )
Also, the function is defined for all real values of x.
i.e. The domain of such a function is: All real numbers.
The function f(x) is given by:
[tex]f(x)=\left \lceil 2x \right \rceil-1[/tex]
Hence, the domain is all the real numbers.
