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Homework Help: Inverse Tan Function

  1. Feb 24, 2009 #1
    1. The problem statement, all variables and given/known data

    State the range

    y=inverse tan( 2x)
    3. The attempt at a solution

    The original range of inverse tan is ( -pi/2, pi/2)

    Should tan inverse (2x) have (-pi, pi) as its range?
  2. jcsd
  3. Feb 24, 2009 #2


    User Avatar
    Science Advisor

    No. 2x changes x values, the domain, not the range. The range of tan-1(x) is (-pi/2, pi/2) because as x goes to negative infinity, tan-1[/sup](x) goes to -pi/2 and as x goes to infinity, tan-1(x) goes to pi/2.

    As x goes to -infinity, what does 2x go to? What does tan-1
    (2x) go to?
    As x goes to infinity, what does 2x go to? What does tan-1
    (2x) go to?
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