1. The problem statement, all variables and given/known data Suppose f is bijection. Prove that f⁻¹. is bijection. 2. Relevant equations A bijection of a function occurs when f is one to one and onto. I think the proof would involve showing f⁻¹. is bijective, by showing f⁻¹ is onto, and one to one, since f is bijective it is invertible. 3. The attempt at a solution To start: Since f is invertible/bijective f⁻¹ is one-to-one: f:A→B f⁻¹:B→A f(a)=b then f⁻¹(b)=a if f(a)=b f(a)=b' then b=b' So f⁻¹ is one-to-one f⁻¹ is onto: *for f to be onto: f:A→B ∀a∈A,∃b∈B f(a)=b * f⁻¹:B→A ∀b∈B,∃a∈A f(b)=a So f⁻¹ is onto. Therefore f⁻¹ is bijective. Would this be correct? Thank You Very Much.