Combine studied function types arithmetically to build models.
Form a function sum and intersect the domains
Problem
For \(f(x)~=~x^2\) and \(g(x)~=~3x~+~5\), find \((f~+~g)(x)\) and its shared domain.
Big Picture
What this problem is really about
A function sum pairs the two outputs produced by the same input; it does not merge the input rules themselves. Write both expressions side by side, combine only like terms, and remember that the new function is available only where both originals are defined. Here the function types make that domain check straightforward.
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