We have to show that

[F(α)G(β)] ^{– 1} = G( – β) F( – α)

We have already shown that

[G (β)] ^{– 1} = G( – β)

[F (α)] ^{– 1} = F( – α)

And LHS = [F(α)G(β)] ^{– 1}

= [G (β)] ^{– 1} [F (α)] ^{– 1}

= G( – β) F( – α)

Hence = RHS