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?

00:10 First, let's see if the function has a domain. If yes, what would it be?

00:15 To find the domain, remember: division by zero is not allowed.

00:20 So, let's find what makes the denominator equal to zero.

00:25 We can take the square root to remove the exponent.

00:29 Now, let's isolate the variable X.

00:42 And there we have it! That's the solution to our 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, $x\ne1$