Combine standard function types arithmetically to create models.
Evaluate an arithmetic combination of functions
Problem
For \(f(x)=x^{2}+3\) and \(g(x)=2x-1\), evaluate \((f+g)(2)\). Show \(f(2)\) and \(g(2)\) separately, add those outputs, and confirm that \(2\) belongs to both function domains.
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What this problem is really about
Evaluating a function combination means using the same allowed input in each component before performing the outside operation. We’ll confirm the shared domain, calculate the two outputs separately, and add those values only after both substitutions are complete.
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