Work with your partner to determine if another input is not allowable for 1x.

In this relation, blank is not an allowable input. Therefore, the domain does not include blank.

1 answer

In the context of functions and relations, the domain refers to the set of all possible input values (or "x-values") that can be used without leading to undefined or non-allowable outputs.

If you are analyzing the input for the relation \(1x\) (which I assume refers to the function \(f(x) = x\)), the only problematic input typically is when dealing with special cases, such as division by zero or taking the square root of a negative number.

In the case of \(f(x) = x\):

  1. Blank: As you mentioned, a blank input is not allowable because it does not represent a valid numerical value.

  2. Other Considerations:

    • If we're just dealing with \(f(x) = x\), theoretically, any real number is permissible as an input.
    • However, if you are employing this function in a wider context (for example, as part of a set of equations or applications), other restrictions might come into play (e.g., if \(x\) represents a quantity that cannot be negative or a certain value specific to a problem).

Thus, while the function \(f(x) = x\) itself has a domain of all real numbers \(\mathbb{R}\), any context clues or additional constraints you have will determine any specific "non-allowable" inputs.

If you have specific conditions or contexts in mind, please share, and I can help clarify what inputs might also be considered non-allowable.