1.
f(x) = 1/4x +5
g(x) = 4x-20
Find fog:
fog: f(g(x)) = f(4x-20)
= 1/4(4x-20)
= x-5 +5
= x
Find gof:
gof: g(f(x)) = g(1/4x+5)
=4(1/4x +5) -20
=x +20 -20
= x
Since fog and gof equal the same they commutative.
2.
f(x) = 2x+4
g(x) = x^2-3
fog = f(x^2-3)
= 2(x^2-3) +4
= 2x^2 -6 + 4
= 2x^2 -2
gof = g(2x+4)
=(2x+4)^2 -3
= 4x^2 +16x +13
fog does not equal gof so is not commutative.