Represent constraints and systems, then interpret viable and non-viable solutions in modeling contexts.
Classify why a constraint-set intersection is empty
Problem
Determine the real viable set for \(\sqrt{x~-~3}~<~0\) and explain the source of feasibility or infeasibility.
Big Picture
What this problem is really about
Separate the radical's input domain from its output range. A real principal square root accepts only inputs with a nonnegative radicand and returns only nonnegative outputs. Compare that actual output set with the inequality's required output set; if they do not overlap, the feasible set is empty without any need for unsafe squaring.
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