Question

Let a function f A B be defined by f(x) 11 B-1-2, 1, 0,2- 4¹5) 0. can you make it one to one and onto both? x-1 F x*-2 with A = {-1, 0, 1, 2, 3, 4) and x+2 find the range off. Is the function one to one and onto both? If not, how a whother each of the functions below is one to one, onto both?​

Answer 1

The function f: A -> B is defined by:

f(x) = { 11, if x = -1 or x = 2,

-1, if x = 0,

-2, if x = 1,

0, if x = 3 or x = 4 }

The range of the function is the set of all possible values of f(x). In this case, the range of f is B = {-2, -1, 0, 11}.

To determine if the function is one-to-one, we need to check if each element in the range has only one pre-image. In other words, we need to check if no two elements in A map to the same element in B. Since each element in B has a unique pre-image in A, the function is one-to-one.

To determine if the function is onto, we need to check if each element in B is the image of some element in A. In this case, every element in B is the image of exactly one element in A, so the function is onto.

Therefore, the function f is one-to-one and onto both.