Mathematics

Problem

Starting with the basic function

y=e^{x}

, the following transformations are performed in order: (a) reflection in the

y

-axis, (b) vertical stretch by a factor of

2

, (c) downward translation by

7

units. Let the resulting function be

p(x)

. a. (i) Write an explicit expression for

p(x)

. b. (ii) Find the domain and range of

p

. c. (iii) Obtain the inverse function

p^{-1}(x)

and state its domain and range.