F(x)=e^2x-4
determine inverse of given function

Step-by-step explanation:

Start by changing the f(x) into a y.  Then switch the x and the y.  Then solve for the new y.  Like this:

becomes

To solve for the new y, we need to get it out of its current exponential position which requires us to take the natural log of both sides.  Since a natural log has a base of e, natural logs and e's "undo" each other, just like taking the square root of a squared number.  

When the ln and the e cancel out we are left with

ln(x) = 2y - 4.  Add 4 to both sides to get

ln(x) + 4 = 2y.  Divide both sides by 2 to get

.

Since that is the inverse of y, we can change the y into inverse function notation:

is there answer choices?