Domain of g(x)

g(x)= sqrt(3-(sqrt(25-x^2))

I got -5, -4, 4, and 5.

I wrote it like [-5, -4] U [4, 5]

I don't think that's right?

3 answers

Under the overall square root you have

3 - square root of 25-x^2

What is under the radical sign has to be positive.

Domain is the X values that will result in a solution and not undefined.

It looks like you can have x=-5 and x =5 because that will give a square root of 0 to subtract from 3. That works. I see that your -4 and 4 also will work.

Those values are included and you used the [ ] instead of ( ) so that is correct and you used the U and that is correct because both sets of the values work. You wouldn't want an intersection.

I agree with your answer.

It could also be written as

-5 =<x=< -4 or 4 =< x =<5

but most likely your teacher wants interval notation whihc your provided.

Thank you!

You are welcome!