Bijection, inverse functions and composition Consider two functions: f: Z Z defined by f(n) = 3n...

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Bijection, inverse functions and composition Consider two functions: f: Z Z defined by f(n) = 3n 2 g: RR defined by g(x) = 3x - 2 (a) Prove that f is not onto. (b) Prove that g is a bijection. (c) Find the inverse of g. (d) Calculate g- og and go g-. (e) What can you say about the result of composing a function with its inverse (gog-) and composing the inverse of a function with itself (g- o g)? Bijection, inverse functions and composition Consider two functions: f: Z Z defined by f(n) = 3n 2 g: RR defined by g(x) = 3x - 2 (a) Prove that f is not onto. (b) Prove that g is a bijection. (c) Find the inverse of g. (d) Calculate g- og and go g-. (e) What can you say about the result of composing a function with its inverse (gog-) and composing the inverse of a function with itself (g- o g)?