How do you find the inverse of $y=ln(3x+1)$ ?

Question

9055 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-07-11T09:11:43

$F^(-1)(x)=y=1/3(e^x-1)$

An inverse function can be found by swapping the x and y around

Like below,
$f(x)=In(3x+1)$

To find the inverse function, you would write:

$x=In (3y+1)$ and then you would solve for y (make y your subject)

$x=log_e (3y+1)$

$e^x=3y+1$

$e^x-1=3y$

$F^(-1)(x)=y=1/3(e^x-1)$

How do you find the inverse of y=ln(3x+1)y=ln(3x+1)?