# Math Help - Finding the domain of a function.

1. ## Finding the domain of a function.

Hello,

My professor gave us a sample worksheet on function domains to use as a study guide for our exam tomorrow, but didn't give us an answer key (so it's really quite useless)! I can't seem to get ahold of her, so I thought I'd post it on here and see if I could get some answers!

Find the domain of the following:

1.) f(x) = 5x-2/7-11x
2.) f(x) = 3-x/x^2+4x+3
3.) f(x) = x^2-9
4.) f(x) = square root of 5-2x
5.) f(x) = cube root of 3x-1
6.) f(x) = 5x+1/eighth root of x-4
7.) f(x) = x+2/seventh root of 5x-10
8.) f(x) = square root of x^2-81
9.) f(x) = square root of 100-x^2
10.) f(x) = square root of x^2-5x+6
11.) f(x) = 9x-1/square root of x^2-5x+6

Below are the answers I got (not sure if they're correct!):

1. (-infinity, 7/11) U (7/11, infinity)
2. (-infinity, -3) U (-3, -1) U (-1, infinity)
3. (-infinity, infinity)
4. (-infinity, 5/2]
5. (-infinity, infinity)
6. (4, infinity)
7. (-infinity, infinity)
8. (-infinity, -9) U (9, infinity)
9. Wasn't sure how to answer this one!
10. (-infinity, 2) U (3, infinity)
11. (-infinity, 2) U (3, infinity)

1-6: good
7: almost. You still can't divide by zero...
8: you should have ] and [
9: really? How did you do all the others?
10: need ] and [

7 is incorrect, think about the denominator more carefully
8 is slightly incorrect, consider the end points of your intervals again
9.. for this one we just have to make sure that we aren't taking the square root of a negative number. In other words, make sure $100-x^2\geq 0$

10 is slightly incorrect, consider the end points of your intervals again

i think the others are good