anonymous
  • anonymous
How do you find the domain of the function f and of its inverse function f-1? f(x) = cos(x - 2) + 7
Mathematics
katieb
  • katieb
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Owlfred
  • Owlfred
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mathteacher1729
  • mathteacher1729
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?"
anonymous
  • anonymous
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.

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anonymous
  • anonymous
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
anonymous
  • anonymous
thank you both. I didnt know it was possible for a function not to have an inverse.
anonymous
  • anonymous
in which case you would say "restrict the domain to \[(2,\pi+2)\] and then this thing would be one to one
mathteacher1729
  • mathteacher1729
Have you tried graphing the function?
anonymous
  • anonymous
i dont really know how to graph it
anonymous
  • anonymous
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.
mathteacher1729
  • mathteacher1729
TO GRAPH ANYTHING 1) go to http://www.wolframalpha.com 2) type " plot y = cos(x-2) + 7 There it is. :)
anonymous
  • anonymous
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.
anonymous
  • anonymous
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
anonymous
  • anonymous
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
anonymous
  • anonymous
\[f^{-1}(x)=cos^{-1}(x-7)+2\]
anonymous
  • anonymous
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)
anonymous
  • anonymous
okay and then the inverse would be (-2, pi -2)?
anonymous
  • anonymous
I'm sorry..I'm slow in math
anonymous
  • anonymous
hello?

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