Answer to Question #255917 in Discrete Mathematics for htd

Question

Let f be the function from x ={0, 1, 2, 3, 4, 5} to X defined by f(x) = 4x mod 6.

Write f as a set of ordered pairs and draw the arrow diagram of f . Is f one-to-one? Is f onto?

Answer 1

The given function as the set of ordered pairs

f = {(0,0), (1,4), (2,2), (3,0), (4,4), (5,2)}

Picture below represents arrow diagram of f

The function is called one-to-one if each x from the domain has exactly one image in the range, and no y in the range is image of more than one x from the domain. As we can see, 0 is the image of both 0 and 3, so the function is not one-to-one.

The function is called onto if every y in the range is the image of at least one x from the domain. As we can see from diagram above, this function is onto.