What is the Composition of Functions f o f?

[nicnicman]

Homework Statement

Let g : A → B and f : B → C where A = {a,b,c,d}, B = {1,2,3}, C = {2,3,6,8}, and g and f are defined by g = {(a,2),(b,1),(c,3),(d,2)} and f = {(1,8),(2,3),(3,2)}.

Find f o f

Homework Equations

The Attempt at a Solution

I know how to find f o g by working from g to f, but I'm not sure what to do with f o f. Does it simply map back to it self?

Thanks for any suggestions.

 

[micromass]

The map f\circ f doesn't even make sense in this context. I think they made an error in the problem statement.

 

[nicnicman]

Well actually it's f o f ^-1, but I just wanted help with the f o f part.
Could you elaborate why this wouldn't make sense?

 

[Dick]

Well actually it's f o f ^-1, but I just wanted help with the f o f part.
Could you elaborate why this wouldn't make sense?

What is f o f(1)?

 

[nicnicman]

(f o f)(1) = f(f(1)) = I want to say 8, but I don't think this is right.

I think f(1) = 8.

 

[SammyS]

(f o f)(1) = f(f(1)) = I want to say 8, but I don't think this is right.

I think f(1) = 8.

So, you're saying f(f(1)) = f(8).

Now to finish answering Dick's question ... What is f(8) ?

 

[nicnicman]

I'm not really sure.

 

[micromass]

Not sure.

Look in your table for f. Search for a couple (8,x). What is x?

 

[Dick]

I'm not really sure.

You probably aren't sure because 8 isn't in the domain of f. Wouldn't this indicate a "doesn't make sense" response?

 

[nicnicman]

Okay so we would mapping from 1 to 8, but then since 8 is not in the domain of f it doesn't work.

 

[micromass]

Okay so we would mapping from 1 to 8, but then since 8 is not in the domain of f it doesn't work.

Indeed. We can go from 1 to 8. But then we can't apply f anymore since we can't leave from 8.

 

[nicnicman]

Okay, thanks for walking me through that.