Range (Mathematics)

In mathematics, the range of a function is the set of all values produced by a function. Sometimes called the image. Given a function f\colon A\rightarrow B, the set f(A) is called the range of f. The range is not to be confused with the codomain B. Generally the range is only a subset of the codomain.

Example

Let the function f be a function on the real numbers:
f\colon \mathbb{R}\rightarrow\mathbb{R}
defined by
f\colon\,x\mapsto x^2
The codomain of f is R, but clearly f(x) never takes negative values, and thus the range is in fact the set R+—non-negative reals, i.e. the interval [0,∞):
0\leq f(x)<\infty.

See also

codomain, domain (mathematics), injective function, surjective function, bijective function

 

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