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

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Answer 1 · 2018-04-28T00:35:16

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

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!