Respuesta :

harpazo

Let y = f(x)

y = ln(3x)

Exchange place with x and y.

x = ln(3y)

Solve for y.

y = (e^x)/3

Replace y with the inverse notation.

f^(-1) x = (e^x)/3

Done.



Answer:

[tex]f^{-1}(x)= \frac{e^x}{3}[/tex]

Step-by-step explanation:

f(x)= ln(3x)

First we replace f(x) with y

y=ln(3x)

Now , interchange the variables x  and y

x= ln(3y)

Solve the equation for y

We know ln has base 'e'

e^x = 3y

divide by 3 on both sides

[tex]y= \frac{e^x}{3}[/tex]

[tex]f^{-1}(x)= \frac{e^x}{3}[/tex]