If k : R → R, k(x) = x2 + 3x – 12; then ‘ determine the type of

1.	If k : R → R, k(x) = x2 + 3x – 12; then ‘ determine the type of the function k.
Answer» 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.

If k : R → R, k(x) = x2 + 3x – 12; then ‘ determine the type of the function k.

Answer»

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.