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If:

$$f(x) = \frac { 2 }{ 3 } x-6 $$

...and $f(g(x)) = x$, then which of the following is $g(x)$?

$ \cfrac { 2 }{ 3 } -\cfrac { 6 }{ x } $

$ \cfrac { 2 }{ 3 } -6x $

$ \cfrac { 3 }{ 2 } x+6 $

$ \cfrac { 3 }{ 2 } x-9 $

$ -\cfrac { 3 }{ 2 } x+6 $