Determine the Domain of the Rational Function 12/(8x-4)

Question

Given the following function:

$\frac{12}{8x-4}$

What is the domain of the function?

00:00 Does the function have a domain? And if so, what is it?

00:03 To find the domain, remember that division by 0 is not allowed

00:07 So let's find the solution that makes the denominator zero

00:10 Let's isolate X

00:26 Let's factor 8 into 4 and 2

00:29 Let's reduce what we can

00:32 And this is the solution to the question

To find the domain of the function $\frac{12}{8x-4}$ , we must determine when the denominator equals zero and exclude these values.

Step 1: Set the denominator equal to zero and solve for $x$ :

$8x - 4 = 0$

Step 2: Solve the equation $8x - 4 = 0$ for $x$ :

Add 4 to both sides: $8x = 4$

Divide both sides by 8: $x = \frac{4}{8} = \frac{1}{2}$

Step 3: The value $x = \frac{1}{2}$ is where the denominator becomes zero, so this value is excluded from the domain.

Therefore, the domain of the function is all real numbers except $x = \frac{1}{2}$ .

The domain of the function is $\boxed{x \ne \frac{1}{2}}$ .

$x\ne\frac{1}{2}$