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.

Domain & Range

Compute the domain and range of a mathematical function.

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

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Continuity

Determine the continuity of a mathematical function.

#### Locate discontinuities of a function:

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Special Functions

Compute properties of multiple families of special functions.

#### Do computations with special functions:

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Injectivity & Surjectivity

Determine the injectivity and surjectivity of a mathematical function.

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

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Periodic Functions

Compute the period of a periodic function.

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

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Number Theoretic Functions

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

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### RELATED EXAMPLES

• Calculus & Analysis
• Continued Fractions
• Differential Equations
• Polynomials
• Rational Functions
• ### Even & Odd Functions

Determine the parity of a mathematical function.

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

Representation Formulas

Compute alternative representations of a mathematical function.

#### Find representations of a function of a given type:

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