Question

Can someone plz give me the answer for this question?

Answer 1

Answer:

see explanation

Step-by-step 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 = $\frac{ln(x+4)}{2}$, that is

$f^{-1}$ (x) = $\frac{ln(x+4)}{2}$