Question

Let a=1,2,3,4 and b =8,9,10 . define a function f a b : → as follows.

(a) is f a surjection?
(b) what is the range of f ? f f f f (1 8, 2 9, 3 9, 4 8

Answer 1

The function f is not a surjection because the element 10 in set B does not have a pre-image in set A under the function f. The range of the function f is {8, 9}.

Step-by-step explanation:

The student is asking whether a certain function f from set A to set B is a surjection, and what the range of f is, given the particular pairs from elements of set A to elements of B.

(a) To determine if f is a surjection, we must verify if every element in B has at least one pre-image in A under the function f. The function f is given by the mapping f(1)=8, f(2)=9, f(3)=9, f(4)=8. Since all the elements in B, which are {8, 9, 10}, are not mapped to from A (10 is missing a pre-image), the function f is not a surjection.

(b) The range of a function is the set of all outputs that the function takes for all inputs from the domain. In this case, since the outputs given are {8, 9, 8, 8}, the range of f is {8, 9}.