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 $y$ :

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

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