Combine standard function types arithmetically to create models.
Determine the domain of a combined function such as (f+g)(x)
Problem
Determine the domain of the combined function \((f+g)(x)\) if \(f\) has domain all real numbers and \(g\) has domain \(x\ge~2\).
Big Picture
What this problem is really about
A function sum needs both component outputs, so its domain is the intersection rather than the union of their domains. We’ll compare the two allowed-input sets, retain only their overlap, and preserve whether the boundary input is included.
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