Question

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

Answer 1

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!