Given that P = \{ x : \;{x is a factor of 6}\; \} is the domain of g(x) = x² + 3x - 5, find the range of x.

Correct Answer is : {-1, 5, 13, 49}

Correct Answer is : {-1, 5, 13, 49}

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WAEC Further Mathematics 2010 Paper

Question : 16

Total: 40

Given that

P = \{ x : \;\text{x is a factor of 6}\; \}

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

, find the range of x.

Solution:

Concept:

The range is found by applying the function

g(x)

to every element in the domain set

P

Explanation:

The domain is

P = \{ x : \text{x is a factor of 6} \}

So,

P = \{1, 2, 3, 6\}

Given

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

, evaluate it for each domain value.

For

x = 1

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

For

x = 2

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

For

x = 3

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

For

x = 6

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

Thus, the set of all output values is the range.

Answer:

\text{Range} = \{-1, 5, 13, 49\}

Correct option: D.

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