Answer:
To determine the inverse of the given function, change f(x) to y, swich x and y, and solve for y.
[tex]f^{-1} (x) = \frac{ln(x+4)}{2}[/tex]
Step-by-step explanation:
To determine the inverse of the given function, change f(x) to y, swich x and y, and solve for y.
Oiriginal function: [tex]f(x) = e^{2x} -4[/tex]
Change f(x) to y: [tex]y = e^{2x} -4[/tex]
Switch x and y: [tex]x = e^{2y} -4[/tex]
Solve for y:
[tex]x = e^{2y} -4[/tex]
[tex]x+4= e^{2y}[/tex]
[tex]ln(x+4)= 2y[/tex]
[tex]y = \frac{ln(x+4)}{2}[/tex]
Then: [tex]f^{-1} (x) = \frac{ln(x+4)}{2}[/tex]
