Problem

For \(x\) items, \(f(x)~=~3x~+~10~\text{dollars}\) is supplier A's cost and \(g(x)~=~2x~+~5~\text{dollars}\) is supplier B's cost. Add the functions to write \((f~+~g)(x)\), then interpret its output.

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What this problem is really about

Function addition combines two complete outputs evaluated at the same input. We’ll place each supplier rule in parentheses, add corresponding variable and constant terms, and keep the common dollar unit throughout. Evaluating the original functions separately at one input and comparing their total with the combined rule checks both the algebra and the contextual meaning.

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(fg)(x) = 6x² + 35x + 50. It adds the supplier costs to give combined cost in dollars.

(f + g)(x) = 5x + 15. It gives the combined number of items.

(f + g)(x) = 6x + 50. It adds the supplier costs to give combined cost in dollars.

(f + g)(x) = 5x + 15. It adds supplier A's cost and supplier B's cost to give the combined cost for x items, in dollars.

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For \(x\) items, \(f(x)~=~3x~+~10~\text{dollars}\) is supplier A's cost and \(g(x)~=~2x~+~5~\text{dollars}\) is supplier B's cost. Add the functions to write \((f~+~g)(x)\), then interpret its output.

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