Question

What is the correct inverse function for f(x)=ln(3x)?

Answer 1

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 2

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

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

`y= (e^x)/(3)`

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