What is the correct inverse function for f(x) = e2x ?

To solve this problem you must appy the proccedure shown below:

 1. You have the following function given in the problem above:

 f(x)=e^2x

 2. You can rewrite is:

 y=e^2x

 3. Interchange the variables, as below:

 x=e^2y

 3. The inverse of an exponential function is the logarithm function. Thereforem you have:

 ln(x)=ln(e^2y)
 ln(x)=2y

 4.Then, you have:

 y=ln(x)/2

 Therefore, the answer is: 

 f^-1(x)=ln(x)/2