Examples for

# Mathematical Functions

In mathematics, a function is defined as a relation, numerical or symbolic, between a set of inputs (known as the function's domain) and a set of potential outputs (the function's codomain). The power of the Wolfram Language enables Wolfram|Alpha to compute properties both for generic functional forms input by the user and for hundreds of known special functions. Use our broad base of functionality to compute properties like periodicity, injectivity, parity, etc. for polynomial, elementary and other special functions.

Compute the domain and range of a mathematical function.

#### Compute the domain of a function:

#### Compute the range of a function:

#### Compute domain and range of a function of several variables:

Determine the continuity of a mathematical function.

#### Determine whether a function is continuous:

#### Locate discontinuities of a function:

Compute properties of multiple families of special functions.

#### Compute properties of a special function:

#### Numerically evaluate a special function:

#### Do computations with special functions:

Determine the injectivity and surjectivity of a mathematical function.

#### Determine whether a given function is injective:

#### Determine whether a given function is surjective:

Compute the period of a periodic function.

#### Compute the period of a periodic function:

#### Find periods of a function of several variables:

Get information about arithmetic functions, such as the Euler totient and Möbius functions, and use them to compute properties of positive integers.

#### Get information about a number theoretic function:

#### Do computations with number theoretic functions:

### RELATED EXAMPLES

Determine the parity of a mathematical function.

#### Determine whether a function is even or odd:

Compute alternative representations of a mathematical function.