Combine studied function types arithmetically to build models.
Form a function product with domain and supported units
Problem
For \(f(x)~=~x~+~3\) and \(g(x)~=~x~-~2\), simplify \((fg)(x)\), state its shared domain, and state whether any contextual quantity or units are supported.
Big Picture
What this problem is really about
Multiplying functions means multiplying their outputs at a shared input. Keep each expression grouped long enough to distribute every term across every term; that structure prevents a missing cross-product or sign. The product inherits only inputs allowed by both original functions, so confirm the common domain after the algebra is simplified.
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