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anonymous

  • 5 years ago

How do you find the domain of the function f and of its inverse function f-1? f(x) = cos(x - 2) + 7

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  1. Owlfred
    • 5 years ago
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    Hoot! You just asked your first question! Hang tight while I find people to answer it for you. You can thank people who give you good answers by clicking the 'Good Answer' button on the right!

  2. mathteacher1729
    • 5 years ago
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    Domain = "all valid inputs for x". Or to say it another way "what values of x will NOT give you 1/0 or square root of a negative or a log of a number less than or equal to 0?"

  3. anonymous
    • 5 years ago
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    the domain is all real numbers. this function is just about as not one to one as you can get, so it does not have an inverse.

  4. anonymous
    • 5 years ago
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    if you choose you can restrict the domain of cosine to say \[(0,\pi)\] and then it will be one to one and have an inverse. perhaps that is what they are asking you to do, to restrict the domain to give an inverse

  5. anonymous
    • 5 years ago
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    thank you both. I didnt know it was possible for a function not to have an inverse.

  6. anonymous
    • 5 years ago
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    in which case you would say "restrict the domain to \[(2,\pi+2)\] and then this thing would be one to one

  7. mathteacher1729
    • 5 years ago
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    Have you tried graphing the function?

  8. anonymous
    • 5 years ago
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    i dont really know how to graph it

  9. anonymous
    • 5 years ago
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    sure. if the function is not one to one then it does not have a function for an inverse. in some cases you can restrict the domain of your function to make it one to one. for example \[f(x)=cos(x)\] is certainly not one to one but if you restrict it for \[(0,\pi)\] then it is.

  10. mathteacher1729
    • 5 years ago
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    TO GRAPH ANYTHING 1) go to http://www.wolframalpha.com 2) type " plot y = cos(x-2) + 7 There it is. :)

  11. anonymous
    • 5 years ago
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    if you do that in your case here, your function says :subtract 2, take the cosine, then add 7. your inverse would say to do the opposite things in the opposite order : subtract 7, take the inverse cosine, add 2.

  12. anonymous
    • 5 years ago
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    Thank you mathteacher1729 and satellite73!!!!! a lot! I'll try doing the other problem like this and if i need help I'll let u know

  13. anonymous
    • 5 years ago
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    i will write out a possible inverse for you if you like. it would just do exactly the opposite of what this one does, as i wrote in english above

  14. anonymous
    • 5 years ago
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    \[f^{-1}(x)=cos^{-1}(x-7)+2\]

  15. anonymous
    • 5 years ago
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    the domain of your original function would be \[(2, \pi+2)\] and the range would be [6,8] making the domain of your inverse function [6,8] and your range [2, pi+2)

  16. anonymous
    • 5 years ago
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    okay and then the inverse would be (-2, pi -2)?

  17. anonymous
    • 5 years ago
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    I'm sorry..I'm slow in math

  18. anonymous
    • 5 years ago
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    hello?

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