Definition

1. Noun:
   • (Mathematics) The set of all possible input values (the independent variable) for which a given function is defined. This is the collection of numbers you can safely put into the function to get a valid output.

Usage Examples

• Noun:
  • The domain of a function f(x) = 1/x is all real numbers except x = 0.
  • Finding the domain of a function is the first step in analyzing its behavior.
  • For the square root function, the domain of a function is restricted to non-negative numbers.

Advanced Usage

• "Restricting the domain of a function": Limiting the set of input values, often to make a function invertible or to fit a real-world context.
  • By restricting the domain of the function to x ≥ 0, we can find its inverse.
• "Natural domain of a function": The largest possible set of real numbers for which the function's rule produces a real number output.
  • The natural domain of the function g(x) = √(x-2) is [2, ∞).

Variants and Related Words

• Domain (n): Often used as a shorter form of "domain of a function" in mathematical contexts.
  • What is the domain of this equation?
• Codomain (n): The set of all possible output values of a function.
• Range (n): The actual set of output values a function produces from its domain.

Synonyms

• Input set: (Informal) The set of allowed inputs.
• Domain: The standard abbreviated term.

Related Phrases

• Domain and range: A common paired phrase describing the complete input-output relationship of a function.
  • The exercise asked students to identify the domain and range of the graph.

Noun

1. (mathematics) the set of values of the independent variable for which a function is defined