Final answer:
The expression (|x|+1)² is well-defined for all real numbers, as the absolute value ensures no negative inputs to the squaring operation, and squaring a real number is always defined.
Step-by-step explanation:
The expression (|x|+1)² makes sense for all real values of x, because the absolute value |x| is always non-negative, and thus, taking |x| and adding 1 will always yield a positive or zero, which can then be squared without any issues.
In mathematics, when we discuss whether an expression 'makes sense,' we are generally referring to the domain of the expression, or all the values of x for which the expression is defined. The domain of (|x|+1)² is all real numbers because there are no restrictions like division by zero or taking the square root of a negative number (as would be the case in the complex domain).