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.
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Correct Answer: Option D
Explanation:
\(P = {x : \text{x is a factor of 6}} \implies P = {1, 2, 3, 6}\)
\(g(x) = x^{2} + 3x - 5\)
\(g(1) = 1^{2} + 3(1) - 5 = 1 + 3 - 5 = -1\)
\(g(2) = 2^{2} + 3(2) - 5 = 4 + 6 - 5 = 5\)
\(g(3) = 3^{2} + 3(3) - 5 = 9 + 9 - 5 = 13\)
\(g(6) = 6^{2} + 3(6) - 5 = 36 + 18 - 5 = 49\)
\(\therefore Range(g(x)) = {-1, 5, 13, 49}\)
\(P = {x : \text{x is a factor of 6}} \implies P = {1, 2, 3, 6}\)
\(g(x) = x^{2} + 3x - 5\)
\(g(1) = 1^{2} + 3(1) - 5 = 1 + 3 - 5 = -1\)
\(g(2) = 2^{2} + 3(2) - 5 = 4 + 6 - 5 = 5\)
\(g(3) = 3^{2} + 3(3) - 5 = 9 + 9 - 5 = 13\)
\(g(6) = 6^{2} + 3(6) - 5 = 36 + 18 - 5 = 49\)
\(\therefore Range(g(x)) = {-1, 5, 13, 49}\)