Questions: The function h is defined below. h(x) = (x-8)/(x^2-5x-36) Find all values of x that are NOT in the domain of h. If there is more than one value, separate them with commas.

The function h is defined below.

h(x) = (x-8)/(x^2-5x-36)

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

Transcript text: The function $h$ is defined below. \[ h(x)=\frac{x-8}{x^{2}-5 x-36} \] Find all values of $x$ that are NOT in the domain of $h$. If there is more than one value, separate them with commas.

Solution

Solution Steps

To find the values of $ x $ that are NOT in the domain of the function $ h(x) = \frac{x-8}{x^2 - 5x - 36} $, we need to determine where the denominator is equal to zero, as division by zero is undefined. This involves solving the quadratic equation $ x^2 - 5x - 36 = 0 $.

Solution Approach

Set the denominator equal to zero: $ x^2 - 5x - 36 = 0 $.
Solve the quadratic equation for $ x $ to find the values that make the denominator zero.
These values are the ones that are NOT in the domain of $ h $.

Step 1: Set the Denominator to Zero

To find the values of $ x $ that are NOT in the domain of the function $ h(x) = \frac{x-8}{x^2 - 5x - 36} $, we start by setting the denominator equal to zero: \[ x^2 - 5x - 36 = 0 \]

Step 2: Solve the Quadratic Equation

Next, we solve the quadratic equation $ x^2 - 5x - 36 = 0 $. The solutions to this equation are: \[ x = -4 \quad \text{and} \quad x = 9 \]

Step 3: Identify Values Not in the Domain

The values $ x = -4 $ and $ x = 9 $ are the points where the denominator is zero, which means these values are not in the domain of the function $ h $.