G o F = {(1,3)(2,2)(3,2)(4,2)(5,5)(1,1)(2,3)(3,4)(4,5)(5,2)}

[JProgrammer]

So I have the following:

F = {(1,3)(2,2)(3,2)(4,2)(5,5)}
G = {(1,1)(2,3)(3,4)(4,5)(5,2)}

Am I right in saying that F o G would be:

F o G = {(1,3)(2,2)(3,2)(4,2)(5,5)(1,1)(2,3)(3,4)(4,5)(5,2)}

If not, does F o G actually mean?

Thank you.

 

[HallsofIvy]

So I have the following:

F = {(1,3)(2,2)(3,2)(4,2)(5,5)}
G = {(1,1)(2,3)(3,4)(4,5)(5,2)}

Am I right in saying that F o G would be:

F o G = {(1,3)(2,2)(3,2)(4,2)(5,5)(1,1)(2,3)(3,4)(4,5)(5,2)}

If not, does F o G actually mean?

Thank you.

No that is not right. Surely there was a definition of the "composition" of two functions where you first met this concept? (You had, I believe, earlier posted this same "F" asking about $$F^{-1}$$. How could you possibly be dealing with inverse functions without knowing what "composition" is? The inverse function is defined by '$$F o F^{-1}(x)= F^{-1}o F(x)= x$$ for all x'.)

In any case, we can interpret "F = {(1,3)(2,2)(3,2)(4,2)(5,5)}" as meaning that F(1)= 3, F(2)= 2, F(3)= 2, F(4)= 2, and F(5)= 5. G= {(1,1)(2,3)(3,4)(4,5)(5,2)} can be interpreted a meaning that G(1)= 1, G(2)= 3, G(3)= 4, G(4)= 5, and G(5)= 2.

"F o G" means "to each x, first apply G, then apply F to that". Starting with x= 1, G(1)= 1 and F(1)= 3 so F o G(1)= 3. G(2)= 3 and F(3)= 2 so F o G(2)= 2. G(3)= 4 and F(4)= 2 so F o G(3)= 2. G(4)= 5 and F(5)= 5 so F o G(4)= 5. G(5)= 2 and F(2)= 2 so F o G(5)= 2. Written as a set of pairs, F o G= {(1, 3), (2, 2), (3, 2), (4, 5), (5, 2)}.

Now, can you use that to find G o F?