Find the Domain: Understanding 8/(x - 2.5)

Question

Given the following function:

8x212 \frac{8}{x-2\frac{1}{2}}

What is the domain of the function?

Video Solution

Solution Steps

00:07 Does the function have a domain? If it does, let's figure out what it is.
00:13 To find the domain, remember: division by zero is not allowed.
00:18 So, let's find the value that makes the denominator zero.
00:24 We'll need to isolate X to solve this.
00:28 And that's the solution to our question!

Step-by-Step Solution

To determine the domain of the function 8x212 \frac{8}{x - 2\frac{1}{2}} , we'll follow these steps:

  • Step 1: Identify where the denominator is zero.
  • Step 2: Solve for x x in this scenario to find exclusions from the domain.
  • Step 3: Provide the domain, excluding these x x values.

Let's go through the problem step by step:
Step 1: We note that the function is undefined where the denominator equals zero. Thus, set the denominator equal to zero: \begin{align*} x - 2\frac{1}{2} &= 0 \end{align*} Step 2: Solve for x x : \begin{align*} x &= 2\frac{1}{2} \end{align*} Step 3: The domain of the function is all real numbers except 212 2\frac{1}{2} . Therefore, we express the domain as all real numbers x x such that x212 x \ne 2\frac{1}{2} .

Thus, the solution to the problem is x212 x \ne 2\frac{1}{2} .

Answer

x212 x\ne2\frac{1}{2}