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Domain/range of inverse functions

  1. Dec 1, 2009 #1
    1. The problem statement, all variables and given/known data


    Find the domain/range:

    1)cos[arcsin(-2x)]=f(x)
    2)sin[arccos(x)] + 2cos(arcsin(x)]=f(x)
    3)sin[arccos(sin(arccos(x)))]


    2. Relevant equations
    arccos
    domain:{-1,1]
    range[0,pi]
    arcsin
    domain:{-1,1]
    range[-pi/2,pi/2]
    tan
    domain:{-infinity,infinity]
    range[-pi/2,pi/2]
    3. The attempt at a solution



    1)d: -1 < -2x<1
    so domain is [-1/2,1/2]

    How do I find the range? Its supposed to be [0,1]
    2)[-1,1] is the domain

    the range is supposed to be [0,3],but why?


    3)for domain i got [-1,1],but range?
    range Is supposed to be [0,180 degrees],but once again,I'm lost.
     
    Last edited: Dec 1, 2009
  2. jcsd
  3. Dec 2, 2009 #2
    There are several ways to approach this question, how did you find the domain?
    by observation? or trial and error? or did you approach this a more formal way.
    If you attempted by observation or trial and error simply rearrange the equation so it is in terms of x and do the same as what you did for domain (except using the 'f(x)' term) that is your range.
    Showing the exact steps you used to solve the domain would be useful in showing you how to approach the range part
     
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