Mathematics

Problem

Consider the function

g(x)=\dfrac{e^{2x}}{1+e^{2x}}

, defined for all real

x

. a. (i) Show that

g

is a strictly monotonic function on

\mathbb R

. b. (ii) Using the result of part (i), evaluate

g(-2),\,g(0)

and

g(2)

without a calculator. c. (iii) Arrange the three values obtained in part (ii) in descending order, giving suitable justification.