Solutions (Functions Supplement Problems) 2. 3. 1 1 .X1 .X2 ()-1-4 4. Not one-to-one: (2) - (2.38) = 2 Onto: Given ZEZ, ER and f(2)=z One-To-One Let x, *x, 2X, -2x, = $(*)-8(x2) Not Onto: 1,3.5.... (all odd natural numbers) have no pre-images One-To-One BIJECTION Let x= x=-=- =h(x) = n(X) Onto: Given > gEQ*: Q and wil Not one-to-one 8((8.2)) = 8((4,1)) Onto: Given 9 04.q- Where PvP, E P (Definition of rational) P2 So (PP) PxP and g((P.:))-2-9 P2 Not one-to-one f|(2.2)) = f((4,0)) - 4 Onto: Given :2, (3,0) Z Z and f((3,0)) - 2 One-To-One BIJECTION Let S - s = 25, +1-25 +1= f(s)-f(sz) Onto: Given n, EN, , 2n + 1 for some neN (Definition of odd integer) So ", LEN and 5. 56934--- 7. Not one-to-one p(2) - P(3)=0 Onto: p(2) - 0, p(4) - 1 Not one-to-one k(-1) - (1) - 1 Not Onto Negative Numbers have no pre-images 8. Solutions (Functions Supplement Problems) 2. 3. 1 1 .X1 .X2 ()-1-4 4. Not one-to-one: (2) - (2.38) = 2 Onto: Given ZEZ, ER and f(2)=z One-To-One Let x, *x, 2X, -2x, = $(*)-8(x2) Not Onto: 1,3.5.... (all odd natural numbers) have no pre-images One-To-One BIJECTION Let x= x=-=- =h(x) = n(X) Onto: Given > gEQ*: Q and wil Not one-to-one 8((8.2)) = 8((4,1)) Onto: Given 9 04.q- Where PvP, E P (Definition of rational) P2 So (PP) PxP and g((P.:))-2-9 P2 Not one-to-one f|(2.2)) = f((4,0)) - 4 Onto: Given :2, (3,0) Z Z and f((3,0)) - 2 One-To-One BIJECTION Let S - s = 25, +1-25 +1= f(s)-f(sz) Onto: Given n, EN, , 2n + 1 for some neN (Definition of odd integer) So ", LEN and 5. 56934--- 7. Not one-to-one p(2) - P(3)=0 Onto: p(2) - 0, p(4) - 1 Not one-to-one k(-1) - (1) - 1 Not Onto Negative Numbers have no pre-images 8