Find the Domain of 65/(2x-2)²: Analyzing Undefined Points

Question

Given the following function:

$\frac{65}{(2x-2)^2}$

What is the domain of the function?

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

00:04 To find the domain, remember that division by 0 is not allowed

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

00:16 We'll take the root to eliminate the denominator

00:26 Let's isolate X

00:41 And this is the solution to the question

To solve for the domain of the function $\frac{65}{(2x-2)^2}$ , follow these steps:

Step 1: Identify when the denominator $(2x-2)^2$ equals zero because the denominator cannot be zero.
Step 2: Solve the equation $(2x-2)^2 = 0$ . This simplifies to $2x-2 = 0$ .
Step 3: Solve for $x$ by adding 2 to both sides: $2x = 2$ .
Step 4: Divide both sides by 2 to isolate $x$ : $x = 1$ .
Step 5: The value $x = 1$ makes the denominator zero, so it must be excluded from the domain.

Thus, the domain of the function is all real numbers except $x \ne 1$ .

Therefore, the solution to the problem is $x \ne 1$ .

$x\ne1$