Value (mathematics)

In mathematics, value commonly refers to the 'output' of a function. In the most basic case, that of unary, single-valued functions, there is one input (the argument) and one output (the value of the function).
 * Example: If the function $$f$$ is defined by prescribing that $$f(x) = 2x^2-3x+1$$ for each real number $$x$$, then the input 3 will yield the function value 10 (since indeed $$2\cdot3^2-3\cdot3+1 = 10$$).

The function $$f$$ of the example is real-valued, since each and every possible function value is real. On the other hand, it is not injective, since different inputs may yield the same value; e.g., $$f(-1.5) = 10$$, too.

In some contexts, for convenience, functions may be considered to have several arguments and/or several values; also cf. the discussion in the article function. However, strictly seen, this is not an extension, since such functions may be considered as having single families and/or sets as input or output.

Value is also used in other senses, e.g., to specify a certain instance of a variable.
 * Example: $$f(x) = 0$$ for two separate values of $$x$$, namely, for $$x=0.5$$ and for $$x=1$$.