Questions: The function g is defined below. g(x) = (x^2 - 2x - 48) / (x^2 + 4x - 45) Find all values of x that are NOT in the domain of g. If there is more than one value, separate them with commas. x =

The function g is defined below.

g(x) = (x^2 - 2x - 48) / (x^2 + 4x - 45)

Find all values of x that are NOT in the domain of g. If there is more than one value, separate them with commas.

x =

Transcript text: The function $g$ is defined below. \[ g(x)=\frac{x^{2}-2 x-48}{x^{2}+4 x-45} \] Find all values of $x$ that are NOT in the domain of $g$. If there is more than one value, separate them with commas. \[ x= \]

Solution

Solution Steps

To find the values of \( x \) that are not in the domain of the function \( g(x) = \frac{x^2 - 2x - 48}{x^2 + 4x - 45} \), we need to determine when the denominator is equal to zero, as division by zero is undefined. Therefore, we solve the equation \( x^2 + 4x - 45 = 0 \) to find the values of \( x \) that make the denominator zero.

Step 1: Identify the Denominator

The function \( g(x) \) is given by

\[ g(x) = \frac{x^2 - 2x - 48}{x^2 + 4x - 45} \]

To find the values of \( x \) that are not in the domain of \( g \), we need to analyze the denominator:

\[ d(x) = x^2 + 4x - 45 \]

Step 2: Set the Denominator to Zero

We set the denominator equal to zero to find the values that make \( g(x) \) undefined:

\[ x^2 + 4x - 45 = 0 \]

Step 3: Solve the Quadratic Equation

Factoring or using the quadratic formula, we find the roots of the equation:

\[ x = -9 \quad \text{and} \quad x = 5 \]

Final Answer

The values of \( x \) that are not in the domain of \( g \) are

\[ \boxed{x = -9, 5} \]

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