# Nonneg vs. Postive real numbers

1. Jan 11, 2007

### storygeek

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
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?

2. Jan 11, 2007

### cristo

Staff Emeritus
The positive reals are $\{x\in \mathbb{R}:x>0\}$ whereas the nonnegative reals are $\{x\in \mathbb{R}:x \not<0\}=\{x\in \mathbb{R}:x\geq 0\}$. Since ex is never zero, then the range of the function is the positive reals.

Last edited: Jan 11, 2007
3. Jan 11, 2007

### storygeek

thanks a whole bunch