Use function notation, evaluate functions on their domains, and interpret notation in context.
Check domain before evaluating a function
Problem
For the real-valued function \(f(x)=\sqrt{x-2}\), test input \(x=5\) before evaluating.
Big Picture
What this problem is really about
Domain comes before evaluation, because a formula can produce written arithmetic even when the real-valued function forbids the input. We’ll derive the square-root restriction from the entire radicand, test the proposed input against it, and evaluate only if the test passes. The final statement should include the restriction, verdict, and exact value.
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