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

{*x*| *x* ≥ –1}

{*x*| *x* ≥ 1}

{*x*| *x* is an integer}

{*x*| *x* is a real number}

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.

Explore the domain of the step function f(x) = ⌈2x⌉ - 1 in detail. Learn about the ceiling function and how it determines the domain of this specific function. Suitable for advanced high school students and anyone interested in mathematical functions.

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