Let the function f be a function on the real numbers:
defined by
The codomain of f is R, but clearly f(x) never takes negative values. The range is in fact the set R^{+} of nonnegative reals, the interval [0,∞):
One could have defined the function g thus:
While f and g have the same effect on a given number, they are not, in the modern view, the same function since they have different codomains.
The codomain can affect whether or not the function is a surjection; in our example, g is a surjection while f is not.
See also: Function domain
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