For each of the functions below, indicate whether the function is onto, one-to-one, neither or both....
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For each of the functions below, indicate whether the function is onto, one-to-one, neither or both. If the function is not onto or not one- to-one, give an example showing why. (a) f: RR. f(x) = x (b) g: R R. g(x) = x (c) h: ZZ.h(x) = x (d) f: Z Z. f(x) = -4 (e) f: ZZ. f(x) = 5x - 4 (f) f:ZZ f(x) = x - 4 (9) f: ZxzZ+ZxZ, f(x, y) = (x+1, 2y) (h) f: ZxZ+ZxZ, f (x, y) = ([5] , v ) (1) f: ZxZ+ZxZ. f(x,y) = (1,5-2) () f: Zxz ZxZ, f(x, y) = (1-y, 1-x) (k) f: Z+xZ+ Zt. f(x, y) = 2 + y. For each of the functions below, indicate whether the function is onto, one-to-one, neither or both. If the function is not onto or not one- to-one, give an example showing why. (a) f: RR. f(x) = x (b) g: R R. g(x) = x (c) h: ZZ.h(x) = x (d) f: Z Z. f(x) = -4 (e) f: ZZ. f(x) = 5x - 4 (f) f:ZZ f(x) = x - 4 (9) f: ZxzZ+ZxZ, f(x, y) = (x+1, 2y) (h) f: ZxZ+ZxZ, f (x, y) = ([5] , v ) (1) f: ZxZ+ZxZ. f(x,y) = (1,5-2) () f: Zxz ZxZ, f(x, y) = (1-y, 1-x) (k) f: Z+xZ+ Zt. f(x, y) = 2 + y.
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a Not onto not onetoone Explanation The function fx x2 is not onto because for any negative value of ... View the full answer
Related Book For
Discrete and Combinatorial Mathematics An Applied Introduction
ISBN: 978-0201726343
5th edition
Authors: Ralph P. Grimaldi
Posted Date:
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