CS2233 Discrete Mathematical Structures Homework 6 Justify all answers in order to receive full credit. Functions...

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CS2233 Discrete Mathematical Structures Homework 6 Justify all answers in order to receive full credit. Functions (100 points) (1) (30 points) Determine whether each of these functions f: {a, b, c, d} {a, b, c, d} is one-to-one and whether each of these functions is onto: (a) f(a) = b, f(b) = a, f(c) = c, f(d) = d (b) f(a)=b,f(b) = b, f(c) = d, f(d) = c (c) f(a)=d, f(b) = b, f(c) = c,f(d) = d (2) (30 points) Determine whether each of these functions f: R R is a one-to-one correspondence (i.e., onto and one-to-one): (a) -3x+4 (b) -3x+7 (c) (x + 2)(x-1)x (3) (10 point) Find fog and g of where f, g: R R with f(x) = 3x+4 and g(x) = x. (4) (30 points) Give an example of a function from N to N that is: Hint: try using absolute value, floor, or ceiling for part (b). (a) one-to-one but not onto (b) onto but not one-to-one (c) neither one-to-one nor onto CS2233 Discrete Mathematical Structures Homework 6 Justify all answers in order to receive full credit. Functions (100 points) (1) (30 points) Determine whether each of these functions f: {a, b, c, d} {a, b, c, d} is one-to-one and whether each of these functions is onto: (a) f(a) = b, f(b) = a, f(c) = c, f(d) = d (b) f(a)=b,f(b) = b, f(c) = d, f(d) = c (c) f(a)=d, f(b) = b, f(c) = c,f(d) = d (2) (30 points) Determine whether each of these functions f: R R is a one-to-one correspondence (i.e., onto and one-to-one): (a) -3x+4 (b) -3x+7 (c) (x + 2)(x-1)x (3) (10 point) Find fog and g of where f, g: R R with f(x) = 3x+4 and g(x) = x. (4) (30 points) Give an example of a function from N to N that is: Hint: try using absolute value, floor, or ceiling for part (b). (a) one-to-one but not onto (b) onto but not one-to-one (c) neither one-to-one nor onto