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Math Help - Finding the domain of a function.

  1. #1
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    Exclamation 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)

    Thank you in advance!
    Last edited by mr fantastic; November 8th 2011 at 02:39 AM. Reason: Deleted begging etc. from post title.
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  2. #2
    Super Member TheChaz's Avatar
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    Re: *** finding the domain of a function...please help asap!!!!! ***

    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 [
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  3. #3
    Junior Member
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    Re: *** finding the domain of a function...please help asap!!!!! ***

    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
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  4. #4
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    Re: *** finding the domain of a function...please help asap!!!!! ***

    Thank you SO much!!!

    So, would #7 be "(-infinity, 2) U (2, infinity)" and #9 be "(10, infinity)"?
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