Thread: The problem in Functions.

Dear All,

The following is my question:

A function f:{1,2,3,4,} -> {0,1,2,3} is defined by the rule: f(n)=(n+6) mod 4
a. Draw an arrow diagram for this function.

I know how to do it but I do not know how to draw it in here.

b. Is f one-to-one?

Yes, it is.

c. Is f onto?

Yes, it is.

d. Does f^-1 exist? Explain your answer.

I have a problem in this part. Please explain the answer to me.

Cheers,

Originally Posted by turboman

Dear All,

The following is my question:

A function f:{1,2,3,4,} -> {0,1,2,3} is defined by the rule: f(n)=(n+6) mod 4
a. Draw an arrow diagram for this function.

I know how to do it but I do not know how to draw it in here.

:
:

d. Does f^-1 exist? Explain your answer.

I have a problem in this part. Please explain the answer to me.

Cheers,

Does every point in {0, 1, 2, 3} correspond to the image of one and only one point in {1, 2, 3, 4}? (You have already answered this) if so the inverse exists.

Alternativly in terms of the arrow diagram is every point in {1,2,3,4} the end point of one and only one arrow from a point in {1,2,3,4}, if so just reverse the arrows and this defines the inverse function.

CB