Inverse function : The inverse function $f^{-1}$ of a function $f$ that does not map several value to the same value is defined by $f^{-1}(f(x))=x.$ In other words $f^{-1}(y)$ is the $x$ such that $f(x)=y.$ $f^{-1}$ is continuous if $f$ is continuous. If $f$ is differentiable we can calculate the derivative of an inverse function as $\frac{d}{dy}f^{-1}(y)=\frac{1}{f^{\prime}(f^-1(y))}.$ This can for example be used to calculate the derivatives of inverse trigonometric functions.