Inverse function
Notation

While the notation f (x) might be misunderstood, (f (x)) certainly denotes the multiplicative inverse of f (x) and has nothing to do with the inverse function of f. The notation f ⟨ − 1 ⟩ {\displaystyle f^{\langle -1\rangle }} might be used for the inverse function to avoid ambiguity with the multiplicative inverse.

In keeping with the general notation, some English authors use expressions like sin (x) to denote the inverse of the sine function applied to x (actually a partial inverse; see below). Other authors feel that this may be confused with the notation for the multiplicative inverse of sin (x), which can be denoted as (sin (x)). To avoid any confusion, an inverse trigonometric function is often indicated by the prefix " arc " (for Latin arcus). For instance, the inverse of the sine function is typically called the arcsine function, written as arcsin (x). Similarly, the inverse of a hyperbolic function is indicated by the prefix " ar " (for Latin ārea). For instance, the inverse of the hyperbolic sine function is typically written as arsinh (x). The expressions like sin (x) can still be useful to distinguish the multivalued inverse from the partial inverse: sin − 1 (x) = { (− 1) n arcsin (x) + π n: n ∈ Z } {\displaystyle \sin ^{-1}(x)=\{(-1)^{n}\arcsin(x)+\pi n:n\in \mathbb {Z} \}}. Other inverse special functions are sometimes prefixed with the prefix "inv", if the ambiguity of the f notation should be avoided.
keywords:existence, startend:end_checker