Answer
They are inverses.
Work Step by Step
To find the inverse of a function, switch the positions of $x$ and $f(x)/y$.
The parent function is $f(x)=x-6$
Switch the $x$ and $f(x)$.
$x=f(x)-6$
Add six to the other side.
$f(x)=x+6$
The inverse you found matches up with the function, $g(x)$.
