Inverse demand function

In economics, an inverse demand function is the mathematical relationship that expresses price as a function of quantity demanded (it is therefore also known as a price function).^[1]

Historically, the economists first expressed the price of a good as a function of demand (holding the other economic variables, like income, constant), and plotted the price-demand relationship with demand on the x (horizontal) axis (the demand curve). Later the additional variables, like prices of other goods, came into analysis, and it became more convenient to express the demand as a multivariate function (the demand function): ${\displaystyle {demand}=f({price},{income},...)}$, so the original demand curve now depicts the inverse demand function ${\displaystyle {price}=f^{-1}({demand})}$ with extra variables fixed.^[2]