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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:RR is a one-to-one correspondence (i.e., onto and one-to-one): (a) 3x+4 (b) 3x2+7 (c) (x+2)(x1)x (3) (10 point) Find fg and gf where f,g:RR with f(x)=3x+4 and g(x)=x2 (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