Domain of 65/(2x-2)²: Find Valid Input Values

Question

Given the following function:

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

Does the function have a domain? If so, what is it?

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

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

00:08 Therefore, let's find the solution that makes the denominator zero

00:11 Let's take the root to eliminate the exponent

00:18 Let's isolate X

00:32 And this is the solution to the question

The denominator of the function cannot be equal to 0.

Therefore, we will set the denominator equal to 0 and solve for the domain:

$(2x-2)^2\ne0$

$2x\ne2$

$x\ne1$

In other words, the domain of the function is all numbers except 1.

Yes, $x\ne1$