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Nonneg vs. Postive real numbers

  • Thread starter storygeek
  • Start date
7
0
1. Homework Statement
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. Homework Equations
Above


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

Conflict
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?
 

Answers and Replies

cristo
Staff Emeritus
Science Advisor
8,056
72
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:
7
0
thanks a whole bunch
 

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