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Nonneg vs. Postive real numbers

  1. Jan 11, 2007 #1
    1. The problem statement, all variables and given/known data
    If the domain of f is restricted to the open interval (-pi/2,pi/2), then the range of f(x) = e^(tanx) is
    A) the set of all reals
    b the set of positive reals
    c the set of nonnegative reals
    d R: (0,1]
    e none of these
    (from barron's How to prep for ap calc)

    2. Relevant equations

    3. The attempt at a solution
    Range of tanx is all real numbers. The range for e^(x) for all real numbers is positive reals. The answers must be b or c

    The answer sheet states that b is the correct answer. How come? isn't b and c the same? What's the difference between all positive reals and all non negative reals?
  2. jcsd
  3. Jan 11, 2007 #2


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    Staff Emeritus
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    The positive reals are [itex]\{x\in \mathbb{R}:x>0\}[/itex] whereas the nonnegative reals are [itex]\{x\in \mathbb{R}:x \not<0\}=\{x\in \mathbb{R}:x\geq 0\}[/itex]. Since ex is never zero, then the range of the function is the positive reals.
    Last edited: Jan 11, 2007
  4. Jan 11, 2007 #3
    thanks a whole bunch
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