Question

Can someone plz give me the answer for this question?

Answer 1

see explanation

Explanation:

Given

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

let f(x) = y

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

Switch x and y and solve for y, that is

x =
`e^(2y)` - 4 ( add 4 to both sides )

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

Take the ln of both sides

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

Divide both sides by 2

y =
`(ln(x+4))/(2)`, that is

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