Answer:
see explanation
Step-by-step explanation:
Given
f(x) = [tex]e^{2x}[/tex] - 4
let f(x) = y
y = [tex]e^{2x}[/tex] - 4
Switch x and y and solve for y, that is
x = [tex]e^{2y}[/tex] - 4 ( add 4 to both sides )
x + 4 = [tex]e^{2y}[/tex]
Take the ln of both sides
ln(x + 4) = ln [tex]e^{2y}[/tex] = 2y [tex]ln_{e}[/tex] = 2y
Divide both sides by 2
y = [tex]\frac{ln(x+4)}{2}[/tex], that is
[tex]f^{-1}[/tex] (x) = [tex]\frac{ln(x+4)}{2}[/tex]
