How do you find the inverse of #f(x) = 3 ln (x-2)#?

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Answer 1 · 2015-11-25T16:56:31

#f^(-1)(x) = e^(1/3 x ) + 2#

1) Insert #y# for #f(x)#:

#y = 3 ln (x-2)#

2) Switch #x# and #y#:

#x = 3 ln(y - 2)#

3) Divide both sides by #3#:

# 1/3 x = ln(y - 2)#

4) Exponentiate both sides to get rid of the logarithm:

# e^(1/3 x ) = y - 2#

5) Add #2# to both sides of the equation:

#e^(1/3 x ) + 2 = y#

6) Finally, insert #f^(-1)(x)# for #y#:

#f^(-1)(x) = e^(1/3 x ) + 2#