Combine standard functions using arithmetic operations to build models.
Subtract two functions and interpret the result
Problem
For \(x\) items, \(R(x)~=~15x~\text{dollars}\) is revenue and \(C(x)~=~5x~+~40~\text{dollars}\) is cost. Subtract the functions to write \((R~-~C)(x)\), then interpret its signed output.
Big Picture
What this problem is really about
A function difference keeps the written order meaningful, especially when one output is revenue and the other is cost. We’ll subtract the entire second rule with parentheses, distribute the negative sign to every term, and simplify only afterward. The resulting dollar output is signed, so comparing it with zero connects the algebra to the business interpretation.
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