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−1(C), is defined as the set of all elements in A which map into C.
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 number have have a square less than 10, namely 1, 4 and 9.