Would the inverse of f(x)=log base 2 (4x)-2 be g(x)=2^(2x)/4 or 1^(2x)/2 ??

Find the inverse of:  f(x)  =  log₂(4x) - 2.

To make the notation simpler, replace  f(x)  with y:

     y  =   log₂(4x) - 2

Interchange  'x'  and  'y':

     x  =  log₂(4y) - 2

Solve for y:

     x + 2  =  log₂(4y)

which is:

 log₂(4y)  =  x + 2

Write in exponential form:

        4y  =  2^{x + 2}

          y  =  (2^{x + 2}) / 4

--->    y  =  (2^{x + 2}) / 2²

--->    y  =  2^x

So, the inverse function is:  y(x)  =  2^x

I've never embedded source code before :))

See how the inverse is the reflection of the graph about the line y=x

You do need to be careful to watch for restrictions on the domain though :)