In mathematics it is possible to have functions of functions, and functions of functions of functions and so on.
So if f is a function of function g of a variable x, which may be written as f(g(x)) then g is the inner function.
Thus in the function sin(3x2+5), the inner function is (3x2+5). Inner functions are particularly important in calculus (differentiation and integration).
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There are infinitely many functions and it is therefore not possible to list them.
The Fourier series is a specific type of infinite mathematical series involving trigonometric functions that are used in applied mathematics. It makes use of the relationships of the sine and cosine functions.
In mathematics the difference between a function and a relation is that each X-value in a function only has a single Y-value.
In mathematics, unary operations are functions having only one number for an input. These include functions such as finding squares, square roots, and reciprocals for a number.
Inverse functions are two functions that "undo" each other. Formally stated, f(x) and g(x) are inverses if f(g(x)) = x. Multiplication and division are examples of two functions that are inverses of each other.