Question

Involves inverse fuctions

Answer 1

1.
`x`

2.
`y`

3.

`y=(\ln (x+4))/(2)`

Explanation:

Given the function

`f(x)=e^(2x)-4`

To find the inverse function, first change
`f(x)` to
`y:`

`y=e^(2x)-4`

Then, switch
`x` and
`y:`

`x=e^(2y)-4`

and solve for
`y:`

`x+4=e^(2y)\\ \\\ln (x+4)=\ln e^(2y)\\ \\2y=\ln (x+4)\\ \\y=(\ln (x+4))/(2)`