^{2}- 25 = 0

^{2}= 25

^{2}) = √(25)

f(x)=(3x-6)/(x^2-25)

Tutors, sign in to answer this question.

Hi Melyssa!

In order to identify the domain of a function (the possible x values that we can plug into the function), we need to figure out if there are any x values that would violate what I call the "laws of math" dealing with real numbers:

Law #1: You cannot divide by 0

Law #2: You cannot take the square root of a negative number

With that in mind, the domain of any function is all real numbers, EXCEPT any x values would violate those laws.

Are there any values of x that would violate those laws?

There are no square roots in the equation, so we don't have to worry about Law #2.

What about Law #1? We can't divide by 0, so the denominator of the function cannot be equal to 0. Let's figure out what x values would make the denominator equal to 0, and we will know that those x values will NOT be part of the domain (because they would violate the Law about dividing by 0)

x^{2} - 25 = 0

x^{2} = 25

√(x^{2}) = √(25)

x = +/- 5 (remember, the square root of a number can be either positive or negative...)

So, the domain of the function would be all real numbers, except x≠-5 or 5

Already have an account? Log in

By signing up, I agree to Wyzant’s terms of use and privacy policy.

Or

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Your Facebook email address is associated with a Wyzant tutor account. Please use a different email address to create a new student account.

Good news! It looks like you already have an account registered with the email address **you provided**.

It looks like this is your first time here. Welcome!

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Please try again, our system had a problem processing your request.