Question

AP Calculus Question
The domain of f is restricted to the open interval (-(pi/2), (pi/2)); then the range of f(x) = e^tanx is

Answer 1

What is the range of tan(x)?

Answer 2

e^x is always positive. When x is very negative, such as when x is close to -pi/2 and tan(x) approaches negative infinity, e^tan(x) will be very close to zero. When tan(x) becomes large, such as when x is close to pi/2, e^x becomes super-large.

Answer 3

I know the range of tan(x) is all real numbers, if the range of e^x is all positive numbers not including 0 would the answer for the range of e^tanx be "the set of positive reals"?