Lecture 19 : Definition of the natural exponential function [Section 9.2]
19.2
Exponential function
We saw in the previous section that the function is one-one and onto. Thus it has inverse.
19.2.1
Definition:
The exponential function, denoted by exp is the one-one, onto function such that
The exponential function, as defined above is also called the exponential function to the natural base. The properties of the exponential function are given in the next theorem.
19.2.2
Theorem:
The function has the following properties:
(i)
(ii)
The function is differentiable and
(iii)
For
(iv)
The function is strictly increasing and concave upward on
is one-one and onto. Thus it has inverse. 
such that 
has the following properties: 
is differentiable and 
is strictly increasing and concave upward on 
