In mathematical terms, if the [[demand curve|demand function]] is Q<math>{demand} = f(P{price})</math>, then the inverse demand function is P<math>{price} = f<sup>−1^{-1}({demand})</supmath>(Q). The value P inof the inverse demand function is the highest price that could be charged and still generate the quantity demanded Q.<ref>Varian, H.R (2006) Intermediate Microeconomics, Seventh Edition, W.W Norton & Company: London</ref> This is useful because economists typically place price ('''P''') on the vertical axis and quantity ('''demand, Q''') on the horizontal axis in supply-and-demand diagrams, so it is the inverse demand function that depicts the graphed demand curve in the way the reader expects to see.
The inverse demand function is the same as the average revenue function, since P = AR.<ref>Chiang & Wainwright, Fundamental Methods of Mathematical Economics 4th ed. Page 172. McGraw-Hill 2005</ref>
