Positiveness: For every , one has , since the functional equation implies . It results that the exponential function is positive (since , if one would have for some , the intermediate value theorem would imply the existence of some such that . It results also that the exponential function is monotonically increasing.
Positiveness: For every  one has , since the functional equation implies . It results, that the exponential function is positive (since , if one would have for some , the intermediate value theorem would imply the existence of some such that . It results also that the exponential function is monotonically increasing.