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For f: A → B and g: B → C, (g ∘ f)⁻¹ =
ARandom
Bg⁻¹ ∘ f⁻¹
Cf⁻¹ ∘ g⁻¹ (reverse order, like matrix transpose)
Dg ∘ f
Answer & Solution
Correct answer: C. f⁻¹ ∘ g⁻¹ (reverse order, like matrix transpose)
Inverse of composition reverses order: (g ∘ f)⁻¹ = f⁻¹ ∘ g⁻¹. Both must be bijections. Same as inverse of matrix product.
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