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Question;(10) Let A = {q, r, s, t} and B = {17, 18, 19, 20}. Determine which of the following are functions. Explain why or why not.f?A ? B,where f={(q,17),(r,18),(s,19),(t,20)}g?A ? B,where g={(q,17),(q,20),(s,19),(t,20),(r,20)}h?A ? B,where h={(q,17),(r,20),(s,19),(t,20)}k?B ? B,where k={(17,17),(18,17),(19,17),(20,18)}l?A ? A,where l={(q,r),(q,s),(s,r),(t,t)}(10) Give the ranges of each of these functions where sets A and B are as stated in #1:f?A ? B,where f={(q,17),(r,18),(s,19),(t,20)}g?A ? B,where g={(q,17),(s,19),(t,20),(r,20)}h?A ? B,where h={(q,17),(r,20),(s,17),(t,20)}k?B ? B,where k={(17,17),(18,17),(19,17),(20,17)}l?A ? A,where l={(q,r),(r,s),(s,q),(t,t)}(10) State whether each of these functions, where sets A and B are as stated in #1, are one-to-one, onto, both, or neither, and give a brief explanation for each answer:f?A ? B,where f={(q,17),(r,18),(s,19),(t,20)}g?A ? B,where g={(q,17),(s,19),(t,20),(r,20)}h?A ? B,where h={(q,17),(r,20),(s,17),(t,20)}k?B ? B,where k={(17,17),(18,17),(19,17),(20,17)}l?A ? A,where l={(q,r),(r,s),(s,q),(t,t)}(8) Determine all bijections from A into B.A = {q, r, s} and B = {2, 3, 4}A = {1, 2, 3, 4} and B = {5, 6, 7, 8}(10) Which of the following functions from R?R are one-to-one, onto, or both? Prove your answers.f(x)=3x-4g(x)= x^2-2h(x)= 2/xk(x)=ln?(x)l(x)=e^x(12) For each function in parts a through f, state a domain that, if it was the domain of the given function, would make the function one-to-one, and explain your answer. If no such domain exists, explain why not. (Hint: graph the function and use the appropriate line test).f(x)=|x-2|g(x)=x^2-2h(x)=x-4x+7k(x)=x^3+4f(x)=3x-4l(x)=-|3x-6|(12) For each function in parts a through f, state a codomain that, if it was the codomain of the given function, would make the function onto, and explain your answer. If no such codomain exists, explain why not.f(x)=|x-2|g(x)=x^2-2h(x)=x-4x+7k(x)=x^3+4f(x)=3x-4l(x)=-|3x-6|(10) Let f = {(-2, 3), (-1, 1), (0, 0), (1, -1), (2, -3)} andlet g = {(-3, 1), (-1, -2), (0, 2), (2, 2), (3, 1)}. Find:f(1)g(-1)(g?f)(1)(g?f?f)(-1)(f?g)(3)(8) Define q, r, and s, all functions on the integers, by q(n)=n^2+2^n, r(n)=n-7, and s(n)=5n-3. Determine:q?r?sr?s?q(q?s?r)(8)(s?r?q)(2)(10) Consider the functions f, g (both on the reals) defined by f(x)=8x+5 and g(x)=x^2.Show that f is injective.Show that f is surjective.Find f^(-1) (x).Find g?f(x).Find f?g(x).

 

Paper#61050 | Written in 18-Jul-2015

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