general approach of exponential functions before

Question

General approach of Exponential Functions :Before getting to this function let's take a much more general approach to things. Let's begin with b = 0 , b ≠ 1. Then an exponential function is a function in the form,

                                       f( x ) = b ^x

Note that we avoid b = 1 since that would give the constant function, f( x ) = 1 .  We ignore

b= 0 as this would also give a constant function and we ignore negative values of b for the following cause. Let's, for a second, assume that we did let b to be negative and look at the given function.

                                        g( x ) = ( -4)^x

Let's perform some evaluation.

g( 2)= ( -4)² =16            g (1/2) =  ( -4)²   =√   -4 = 2i

hence, for some values of x we will obtain real numbers and for other values of x well we get complex numbers.  We desire to avoid this and thus if we require b = 0 this will not be a problem.