Value (mathematics)
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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) = 2x2 − 3x + 1 for each real number x, then the input 3 will yield the function value 10 (since indeed 2 · 32 – 3 · 3 + 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.
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