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Let f be a function from the set A to the set B. Let S be
Chapter 1, Problem 45E(choose chapter or problem)
Problem 45E
Let f be a function from the set A to the set B. Let S be a subset of B. We define the inverse image of S to be the subset of A whose elements are precisely all pre - images of all elements of S. We denote the inverse image of S by , so
{a
A |
}. (Beware: the notation
is used in two different ways. Do not confuse the notation introduced here with the notation
for the value at y of the inverse of the invertible function f. Notice also that
, the inverse image of the set S, makes sense for all functions f, not just invertible functions.)
Let f be a function from A to B. Let S be a subset of B. Show that
Questions & Answers
QUESTION:
Problem 45E
Let f be a function from the set A to the set B. Let S be a subset of B. We define the inverse image of S to be the subset of A whose elements are precisely all pre - images of all elements of S. We denote the inverse image of S by , so
{a
A |
}. (Beware: the notation
is used in two different ways. Do not confuse the notation introduced here with the notation
for the value at y of the inverse of the invertible function f. Notice also that
, the inverse image of the set S, makes sense for all functions f, not just invertible functions.)
Let f be a function from A to B. Let S be a subset of B. Show that
Solution:
Step 1
In this problem we are asked to show that where the inverse image of S is denoted by
and
{a
A |
}.