Exercise 8.12. Determine whether each of the following is invertible. If it is, write down its...

 

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Exercise 8.12. Determine whether each of the following is invertible. If it is, write down its inverse and show that it satisfies Definition 8.16. If it is not, then that means it is either not injective, not surjective, both. If it is not injective, give two distinct values a and y from the function's domain for which f(x) = f(y). If it is not surjective, give an element of the codomain which is not hit by the function. You do not need to prove that your answers are correct. gr (a) k: R→ R where k(x) = +2. (b) f: RR where f(x) = (c) g: R+R where g(x) = x² (d) h: [0, π] → [-1, 1] where h(x) = cos(x) (e) j: [0, π] → [-2, 2] where j(x) = cos(x) (f) k: NZ where k(x) = (-1)" (2n-1)+1 4 Exercise 8.12. Determine whether each of the following is invertible. If it is, write down its inverse and show that it satisfies Definition 8.16. If it is not, then that means it is either not injective, not surjective, both. If it is not injective, give two distinct values a and y from the function's domain for which f(x) = f(y). If it is not surjective, give an element of the codomain which is not hit by the function. You do not need to prove that your answers are correct. gr (a) k: R→ R where k(x) = +2. (b) f: RR where f(x) = (c) g: R+R where g(x) = x² (d) h: [0, π] → [-1, 1] where h(x) = cos(x) (e) j: [0, π] → [-2, 2] where j(x) = cos(x) (f) k: NZ where k(x) = (-1)" (2n-1)+1 4

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Lets analyze each function to determine whether it is invertible and find its inverse if applicable Well also identify whether it is injective surject... View the full answer