Difference between revisions of "Range"
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Let <math>A</math> and <math>B</math> be any sets, and let <math>f:A\to B</math> be any function. Then <math>\{b\in B\mid \mathrm{there\ is\ some\ } a\in A\mathrm{\ such\ that\ } f(a)=b\}</math> is called the '''range''' or '''image''' of <math>f</math>. | Let <math>A</math> and <math>B</math> be any sets, and let <math>f:A\to B</math> be any function. Then <math>\{b\in B\mid \mathrm{there\ is\ some\ } a\in A\mathrm{\ such\ that\ } f(a)=b\}</math> is called the '''range''' or '''image''' of <math>f</math>. | ||
| − | Thus, if we have <math>f: \mathbb{R} \to \mathbb{R}</math> given by <math>f(x) = x^2</math>, the range of <math>f</math> is the set of | + | Thus, if we have <math>f: \mathbb{R} \to \mathbb{R}</math> given by <math>f(x) = x^2</math>, the range of <math>f</math> is the set of [[nonnegative]] reals. |
Revision as of 09:24, 6 July 2006
Let 
and 
be any sets, and let 
be any function. Then 
is called the range or image of 
.
Thus, if we have 
given by 
, the range of is the set of nonnegative reals.
