How do you find the inverse of f(x) = 2log (3x-12) + 5?

1 Answer
Apr 28, 2018

The inverse function f^-1(x) is 10^((x-5)/2)/3+4.

Explanation:

If you let y=2log(3x-12)+5, make a new equation switching the x's and y's and then solve for the new y:

x=2log(3y-12)+5

x-5=2log(3y-12)

(x-5)/2=log(3y-12)

Convert to exponential form:

10^((x-5)/2)=3y-12

10^((x-5)/2)+12=3y

10^((x-5)/2)/3+4=y

That is the inverse function. Hope this helped!