Consider the function

MATHEMATICS · Multi-part · AP · AP Precalculus · Exponential and Logarithmic Functions · Exponential and Logarithmic Functions

Problem

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

, defined for all real

x

. (i) Show that

g

is a strictly monotonic function on

\mathbb R

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

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

and

g(2)

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