The domain of the function f(x) = |x|^2 includes all real numbers. This is because the absolute value function, |x|, is defined for every real number, and raising any real number (including the value of |x|) to the power of 2 is also defined for all real numbers.
To elaborate, for any value of x, whether it is positive, negative, or zero, you can calculate |x|, and then squaring that result will always produce a valid number. Thus, there are no restrictions on the inputs for this function.
In formal terms, we can express the domain as:
Domain: (-∞, ∞)