Question

What is the domain of the step function f(x) = ⌈2x⌉ – 1?

Answer 1

The domain of the given step function is:

The set of all the real numbers.

Explanation:

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:

`f(x)=\left \lceil x \right \rceil`

(

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:

`f(x)=\left \lceil 2x \right \rceil-1`

Hence, the domain is all the real numbers.

Answer 2

f(x) is defined for "all real numbers."