k : R → R
∴ Domain = {…, -3, -2, -1, 0, 1, 2, …}
k (x) = x2 + 3x – 12
∴ k (- 3) = (- 3)2 + 3 (- 3) – 12 = – 12
k (- 2) = (- 2)2 + 3 (- 2) – 12 = 4 – 6 – 12 = – 14
k (- 1) = (- 1 )2 + 3 (- 1) – 12 = 1 – 3 – 12 = -14
k(0) = 0 + 0 – 12 = – 12
k(1) = 1 + 3 – 12 = -8
k (2) = 4 + 12 – 12 = 4
∴ Co-domain = {…, -12, -14, -14, -12, -8, 4, …}
Here, for the elements – 3 and 0, – 2 and – 1 of domain, their images are same. Therefore function k is many-one function.