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Find the domain of the vector functions

  1. Sep 16, 2005 #1
    Find the domain of the vector functions, r(t), listed below

    a.) r(t) = <ln(6t), sqrt(t+14), 1/sqrt(16-t)>

    i dont extactly know how to approach this, can someone give me a hint or two
     
  2. jcsd
  3. Sep 16, 2005 #2
    The domain of a function [tex]f(x)[/tex] basically means the set of all [tex]x[/tex] for which the function yields valid results. In your case, I presume all vector components must be real numbers. What does that mean for the values that [tex]t[/tex] is allowed to have?
     
  4. Sep 16, 2005 #3
    [tex] t \geq -14[/tex]
    [tex] t \leq 16[/tex]

    right? so the domain should be from [-14,16]
     
  5. Sep 16, 2005 #4
    You're on the right track, but what about the ln(6t) function?
     
  6. Sep 16, 2005 #5
    t cannot equal to 0 for ln(6t). so should it be [-14,0) U (0, 16]
     
  7. Sep 16, 2005 #6
    If ln(6t) is to yield a real number, t must be greater than 0. A negative value for t won't work! So one of the domains you posted is almost right - the one holding positive values. The reason that the interval isn't exactly correct is because t = 16 isn't allowed (take a look at the third term and see what happens when t=16). In other words: t is in (0,16) instead of (0,16].
     
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