The notation \( {x \mid -\infty < x < \infty} \) represents the set of all real numbers. This expression describes the domain of a function that includes every possible real number, meaning there are no restrictions on the value of \( x \).
In mathematical terms, the domain can also be expressed as \( \mathbb{R} \), which denotes the set of all real numbers. So yes, this is a valid domain, indicating that \( x \) can take any real value from negative infinity to positive infinity.