Nonneg vs. Postive real numbers

[storygeek]

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)

Homework Equations

Above

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?

 

[cristo]

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 e^x is never zero, then the range of the function is the positive reals.

 

[storygeek]

thanks a whole bunch