Question

If I am given the revenue function r(x)=x(75-3x) and cost function c(x)=124+12x
How do I find profit function p(x)
I thought r(x)=xp (x(profit function)) and tried doing it backwards but no luck with the answer.

Answer 1

Profit = Revenue - Cost
P(x) = R(x) - C(x)

(FWIW, I think you're combining functions. Sometimes they give you a price function, and you use that to find the Revenue function. Revenue = x * price

Answer 2

why isn't it \[r(x)-c(x)\]?

Answer 3

@hapahearthero unfortunately p is confused with profit and price since they start with the same letter

In the case of r(x) = x*p, we have revenue equal to x times price (p)

In the case of P(x) = R(x) - C(x) we have profit (P) equal to the difference of revenue (R) and cost (C)