Commutative Comp. of Functions: Find two functions F and G so that F ∘ G = G ∘ F AND

[Veru]

Commutative Comp. of Functions: Find two functions F and G so that F ∘ G = G ∘ F AND

Hello!

I am working on a question and would like some hints or help on how I should think about this to get started.

The question reads:

In general, function composition is not commutative. F ∘ G does not equal G ∘ F. But some functions do compute. For example, if F and G are inverses, then the two compositions of functions do equal each other. Let's find some more.

Find two functions F and G so that F ∘ G = G ∘ F AND:
>F and G are not inverses of each other
>F does not equal G
>Neither F nor G is the identity function I(x)=x.

I am having trouble coming up with any sort of example and I can't find any other online resources.

Thank you for your help!
Veru

 

[tkhunny]

F = 2
G = 5

Would you also like to throw out F and G being constant?