recall that, to get the inverse relation of any expression, we start off by doing a quick switcharoo on the variables, then we solve for "y".
[tex]\bf \stackrel{f(x)}{y}=-6x+6\qquad inverse\implies \boxed{x}=-6\boxed{y}+6
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x-6=-6y\implies \cfrac{x-6}{-6}=y\implies -\cfrac{x}{6}+1=\stackrel{f^{-1}(x)}{y}[/tex]