Question

Two sets A and B are defined as A = {a, b, c, d] B = {1, 2, 3). Let the function f: A+B be defined as f = {(a, 1), (b, 2), (C, 1), (d, 1)). What are the 1. Domain [Select] [ Select ] 2. Range {1,2} {1,2,3) {a,b] 3. Target {a,b,c,d} of this function?

Answer 1

In the function f from set A to B, the domain is {a,b,c,d}, the range is {1,2}, and the target is the entire set B which is {1,2,3}.

Step-by-step explanation:

To answer the student's question, firstly we specify the terms related to functions. The domain of a function is the set of all possible input values which the function can accept. The range is the set of all possible output values that the function can provide, based on the input from the domain. The target is the set that the output values of the function are drawn from, which may include values that are never reached by the function.

In the given function f: A → B, the domain is the set A and the range is the subset of B that f actually maps to. The set A is given as {a, b, c, d} and the set B is {1, 2, 3}. The function f is given as f = {(a, 1), (b, 2), (c, 1), (d, 1)}.

1. The domain of this function is {a, b, c, d}.
2. The range of this function is the set of second values in the order pairs of f, which is {1, 2}.
3. The target is the set B, which is {1, 2, 3}. Note that even though 3 is not mapped by any element of A, it is still part of the target set because it is a possible value in set B that outputs from A could potentially map to.