Elementary function

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Elementary function

An elementary function is a function built from a finite number of exponentials, logarithms, real constants, and one variable. The trigonometric functions and their inverses are assumed to be included in the elementary functions by using the relations between the trigonometric functions and the exponential and logarithmic functions.

Examples of elementary functions include the following:

$f(x)=2$	a constant function
$f(x)=x^3$	a power function
$f(x)=\sqrt{x}$	a root function
$f(x)=x^2-9x+3$	a polynomial function
$f(x)=\frac{x^2+2x+3}{x^2+1}$	a rational function
$y=\sin(x)$	a trigonometric function
$y=\arcsin(x)$	an inverse trigonometric function
$y = \ln(x)$	a logarithmic function (specifically, the natural logarithm)
$y=e^x$	an exponential function
$y=\frac{xe^x-\log_2(1+x^2)}{\sqrt{\arctan(3x)}}$	an elementary function combining several of the above types of functions