4. Let f: Z→ Z defined by f(x) = x - 7. Determine the following. a) Domain b) Co-domain c) Range d) Image of 3 e) f) g) Is f one-one? Is f on-to? Is f invertible? If so, find the inverse

Q: 1. Let f : Z6 → Z6 be such that f(7) = x2 + 3. (a) Is f a well defined function? (b) Is f…

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Q: 3. а) Define the following terms as used in graph theory: i) regular graph ii) simple circuit

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Q: Let f:R → R such that f(x) = x² – 2x + 1. Verify whether f is bijective ? explain your answer.

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Q: a) Let f: Z Z be such that f(x) 2*x. Is f invertible, and if so, what is its inverse?

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Q: 5. а) Define the following with an example: i) Domain of a function ii) One – to – one function -…

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Q: 5. Let f:7 → Z defined by f(x) = 4x²-3. Determine the following. a) Domain d) Is f one-one? e) Is…

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Q: Let f : R → R be a function given by f(x) = 2x – 1 (a) Determine whether f is bijective or not. (b)…

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Q: Let LR R be a linear operator such that L X, )-| X1 then Ker(L) spanned by: Select one: a. (e2,e3)…

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Q: Let f.g.h:A - A be any bijective functions. Then (g oh on-

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Q: Let f be the function from R to R with f(x) = 3x - 5. a) Prove in detail that f is one-to-one. b)…

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Q: f: R2 → R, f(x1, x2) = x1-x2 function is given. a) Can f be an surjective function? b) Can f be an…

A: f: R2 → R, f(x1, x2) = x1-x2 function is given. a) Can f be an surjective function? b) Can f be an…

Q: Consider the function g : ZxZ → Z × Z defined by g(x, y) = (4xy, 9x + 5y). (a) Is g injective? (b)…

A: (a) we see (5, 0) and (0, 9) are different elements in ZxZ.      But, g(5, 0) = (4.5.0, 9.5+5.0) =…

Q: 3. Assume f:{-3,0, 2, 11}{-11,0, 3, 5, 19} be a function given by f(-3) = 0, f(0) = -11,ƒ(2) =…

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Q: or the given function f(x) = [3x + 5], compute f ({2}).

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Q: 4) Consider the function g(x) = [2r – 1] where g : R → Z. a) Is g a one-to-one function? Explain. b)…

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