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