(a) Let let and let be given by i) Is finjective? Briefly explain. ii) Is f...

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(a) Let let and let be given by i) Is finjective? Briefly explain. ii) Is f surjective? Briefly explain. iii) Is f'bijective? Briefly explain. v) Let (b) Let iv) Does f have an inverse function? Briefly explain. and let A = {x € Nx ≤ 6), Prove that B = {x € Nx ≤ 50}, f: A → B -> C = {x €N|20 <x<50}. What is f¹(C), where f¹(C) denotes the inverse image of the set C? f(x) = x² + x + 1. Hint: You need to show that f: A → B C₁ ≤ A and C₂ A. f(C₁n C₂) ≤ f(C₁) Nf(C₂). y = f(C₁C₂) =y=f(C₁) Nf(C₂). (a) Let let and let be given by i) Is finjective? Briefly explain. ii) Is f surjective? Briefly explain. iii) Is f'bijective? Briefly explain. v) Let (b) Let iv) Does f have an inverse function? Briefly explain. and let A = {x € Nx ≤ 6), Prove that B = {x € Nx ≤ 50}, f: A → B -> C = {x €N|20 <x<50}. What is f¹(C), where f¹(C) denotes the inverse image of the set C? f(x) = x² + x + 1. Hint: You need to show that f: A → B C₁ ≤ A and C₂ A. f(C₁n C₂) ≤ f(C₁) Nf(C₂). y = f(C₁C₂) =y=f(C₁) Nf(C₂).

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ANSWER i To determine if f is injective we need to check if different elements in A map to different elements in B In other words if fx1 fx2 then x1 x... View the full answer