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 is D

\(P = {x : \text{x is a factor of 6}} \implies P = {1, 2, 3, 6}\)

\(g(x) = x^{2} + 3x - 5\)

\(g(1) = 1^{2} + 3(1) - 5 = 1 + 3 - 5 = -1\)

\(g(2) = 2^{2} + 3(2) - 5 = 4 + 6 - 5 = 5\)

\(g(3) = 3^{2} + 3(3) - 5 = 9 + 9 - 5 = 13\)

\(g(6) = 6^{2} + 3(6) - 5 = 36 + 18 - 5 = 49\)

\(\therefore Range(g(x)) = {-1, 5, 13, 49}\)