Definition:Elementary Function

Definition

An elementary function is one of the following:

• The constant function: $f_c \left({x}\right) = c$ where $c \in \R$

• Powers of $x$: $f \left({x}\right) = x^y$, where $y \in \R$

• Exponentials: $f \left({x}\right) = e^x$

• Natural logarithms: $f \left({x}\right) = \ln x$

• Trigonometric functions: $f \left({x}\right) = \sin x$, $f \left({x}\right) = \cos x$

• Inverse trigonometric functions: $f \left({x}\right) = \arcsin x, f \left({x}\right) = \arccos x$

• All functions obtained by replacing $x$ with any of the functions above, e.g. $f \left({x}\right) = \ln \sin x, f \left({x}\right) = e^{\cos x}$

• All functions obtained by adding, subtracting, multiplying and dividing any of the above types any finite number of times.