The domain of the step function $f(x) = \lceil 2x \rceil - 1$ is the set of all possible values of $x$ for which the function is defined.

The function $\lceil 2x \rceil$ represents the ceiling function, which rounds $2x$ up to the nearest integer. Since the ceiling function is defined for all real numbers, the expression $\lceil 2x \rceil - 1$ is also defined for all real numbers.

Therefore, the correct answer is:

{x | x is a real number}

Would you like more details on this, or do you have any other questions?

Here are some related questions:

1. What is the range of the function $f(x) = \lceil 2x \rceil - 1$?
2. How does the ceiling function $\lceil x \rceil$ differ from the floor function $\lfloor x \rfloor$?
3. Can a step function like $f(x) = \lceil 2x \rceil - 1$ ever be continuous?
4. How would the graph of $f(x) = \lceil 2x \rceil - 1$ look?
5. What is the effect of multiplying $x$ by 2 before applying the ceiling function?

Tip: When dealing with step functions like ceiling or floor functions, it's important to consider how these functions round numbers and how they affect the overall function.