Inverse function

Up to now we have considered functions $y(x)$ where $y$ is the output variable and $x$ is the input variable. Hence, the value of $y$ depends on the value of $x$. However, sometimes we are also interested in the opposite: we want to know in what way $x$ depends on $y$, or, we want to know the function $x(y)$.

One could think of the relation between price $p$ and quantity $q$. Depending on situation you want to know in what way price depends on quantity (the function $p(q)$) or how quantity depends on price (the function $q(p)$). The function $q(p)$ is called the inverse function of the function $p(q)$ (and vice versa).