Final answer:
The domain of the function f(x) = eˣ * x² is all real numbers.
Step-by-step explanation:
The domain of a function is the set of all possible values that the input (or independent variable) can take. To find the domain of the function f(x) = eˣ * x², we need to determine what values of x are allowed. Since eˣ is always positive for any real value of x, we don't need to worry about it affecting the domain. However, x² can take any real value, so there are no restrictions on the domain. Therefore, the domain of f(x) = eˣ * x² is all real numbers.