Question

Consider the given function.

Answer 1

To determine the inverse of the given function, change f(x) to y, swich x and y, and solve for y.

`f^(-1) (x) = (ln(x+4))/(2)`

Explanation:

To determine the inverse of the given function, change f(x) to y, swich x and y, and solve for y.

Oiriginal function:
`f(x) = e^(2x) -4`

Change f(x) to y:
`y = e^(2x) -4`

Switch x and y:
`x = e^(2y) -4`

Solve for y:

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

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

`ln(x+4)= 2y`

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

Then:
`f^(-1) (x) = (ln(x+4))/(2)`