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

Question

8158 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)#