<P> for all real numbers x . In this example, f can be thought of as the composite of several simpler functions: squaring, adding 1, and taking the sine . However, only the sine function has a common explicit symbol (sin), while the combination of squaring and then adding 1 is described by the polynomial expression x 2 + 1 (\ displaystyle x ^ (2) + 1). In order to explicitly reference functions such as squaring or adding 1 without introducing new function names (e.g., by defining function g and h by g (x) = x 2 (\ displaystyle g (x) = x ^ (2)) and h (x) = x + 1 (\ displaystyle h (x) = x + 1)), one of the methods below (arrow notation or dot notation) could be used . </P> <P> Sometimes the parentheses of the functional notation are omitted, when the symbol denoting the function consists of several characters and no ambiguity may arise, as for </P> <Dl> <Dd> sin ⁡ x instead of sin ⁡ (x). (\ displaystyle \ sin x \ quad (\ text (instead of)) \ quad \ sin (x).) </Dd> </Dl> <Dd> sin ⁡ x instead of sin ⁡ (x). (\ displaystyle \ sin x \ quad (\ text (instead of)) \ quad \ sin (x).) </Dd>

Example of a mapping diagram that is not a function