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

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Answer 1 · 2015-12-06T14:50:10

$F circ G ne G circ F$

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

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

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

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

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

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