Question

If `F(x)= x+2` and `G(x)= x/2`, how do you determine if the composition of functions is commutative?

Answer 1

`F circ G ne G circ F`

Explanation:

`F(G(x)) = F(x/2) = x/2 + 2`

`G(F(x)) = G(x + 2) = (x+2)/2`

They would be commutative if and only if F(G) = G(F), forall x in the domain.

`F(G(0)) = 0/2 +2 = 2`

`G(F(0)) = (0 + 2)/2 = 1`