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

Given the following function:

65(2x−2)2 \frac{65}{(2x-2)^2}

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
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.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Given the following function:

65(2x−2)2 \frac{65}{(2x-2)^2}

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

2

Step-by-step solution

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≠0 (2x-2)^2\ne0

2x≠2 2x\ne2

x≠1 x\ne1

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

3

Final Answer

Yes, x≠1 x\ne1

Practice Quiz

Test your knowledge with interactive questions

Given the following function:

\( \frac{5-x}{2-x} \)

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

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