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saul85 [17]
3 years ago
8

The function is defined below g(x)= (x^2+4x-5)/(x^2-7x+12 Find all values of that are NOT in the domain of . If there is more th

an one value, separate them with commas.
Mathematics
1 answer:
blagie [28]3 years ago
5 0

Answer:

3,4.

Step-by-step explanation:

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

ax^{2} + bx + c, a\neq0.

This polynomial has roots x_{1}, x_{2} such that ax^{2} + bx + c = a(x - x_{1})*(x - x_{2}), given by the following formulas:

x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}

x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}

\Delta = b^{2} - 4ac

In this question:

The function is:

g(x) = \frac{x^2+4x-5}{x^2-7x+12}

In a fraction, the values not in domain are the values for which the denominator is 0.

Find all values of that are NOT in the domain of g.

It will not be in domain if the denominator is 0. So

x^2 - 7x + 12 = 0

That is, a quadratic equation with a = 1, b = -7, c = 12

\Delta = (-7)^{2} - 4(1)(12) = 49 - 48 = 1

x_{1} = \frac{-(-7) + \sqrt{1}}{2(1)} = 4

x_{2} = \frac{-(7) - \sqrt{1}}{2(1)} = 3

The values are 3 and 4, so the answer is 3,4.

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