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Lucy found that a solution of x = - 4 was extraneous for her function. What would be a possible denominator in Lucy's function?

Ax2 + 3x - 4

Bx2 - 9

Cx + 5

Dx - 4

Verified Answer :

metchelle

The correct answer for the given question above would be option A. The possible denominator in Lucy's function in which she found that a solution of x = -4 was extraneous for her function is that, x2 + 3x - 4. For that case, it is the first one since it is the same as (x+4)(x−1) which cannot have x=−4 as that would make the denominator zero. 

Answer:

The answer is A. \(x^2+3x-4\)

Step-by-step explanation:

In order to determine the correct Lucy's function, we need to understand the meaning of solution of the equation.

The solution of a equation is the value of the variable that makes the function gives a zero value.

So, to find the correct function, we replace the value x=-4 in every options. If the function gives zero, so that will be the correct Lucy's function.

Given \(x=-4\)

\(x^2+3x-4\\(-4)^2+3*(-4)-4\\16-12-4\\0\)

\(x^2-9\\(-4)^2-9\\16-9\\7\)

\(x+5\\(-4)+5\\1\)

\(x-4\\(-4)-4\\-8\)

So, the Lucy's function that gives zero value is  \(x^2+3x-4\).

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