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| Example: | Example: | ||
| Take as ] A and B the ] 1, 2, 3,... Take as function f the ] that assigns to every ] its ]. Take as ] C of B all ] less than 10. Then the ''inverse image'' of C consists of the ] 1, 2 and 3, since only these ] |
Take as ] A and B the ] 1, 2, 3,... Take as function f the ] that assigns to every ] its ]. Take as ] C of B all ] less than 10. Then the ''inverse image'' of C consists of the ] 1, 2 and 3, since only these ] have a ] less than 10, namely 1, 4 and 9. | ||
Revision as of 16:33, 11 May 2004
An inverse image in mathematics is defined in the following way:
Consider a function f which maps from some set A to some set B. Let C be a subset of B, then the inverse image of C under the function f, written f(C), is defined as the set of all elements in A which map into C.
Example:
Take as sets A and B the natural numbers 1, 2, 3,... Take as function f the quadratic function that assigns to every number its square. Take as subset C of B all natural numbers less than 10. Then the inverse image of C consists of the number 1, 2 and 3, since only these numbers have a square less than 10, namely 1, 4 and 9.