Given that (P = {x : text{x is a factor of 6}}) is the domain of (g(x) = x^{2} + 3x – 5), find the range of x.
-
A.
{-1, 5, 13} -
B.
{5, 13, 49} -
C.
{1, 2, 3, 6} -
D.
{-1, 5, 13, 49}
Correct Answer: Option D
Explanation
(P = {x : text{x is a factor of 6}} implies P = {1, 2, 3, 6})
(g(x) = x^{2} + 3x – 5)
(g(1) = 1^{2} + 3(1) – 5 = 1 + 3 – 5 = -1)
(g(2) = 2^{2} + 3(2) – 5 = 4 + 6 – 5 = 5)
(g(3) = 3^{2} + 3(3) – 5 = 9 + 9 – 5 = 13)
(g(6) = 6^{2} + 3(6) – 5 = 36 + 18 – 5 = 49)
(therefore Range(g(x)) = {-1, 5, 13, 49})