Question 390987
{{{f(x) = (6/x)-7}}}

   1. Replace {{{f(x)}}} with {{{y}}}.

{{{y= 6/x-7}}}

2. Reverse the roles of {{{x}}} and {{{y}}}, that is replace every occurrence of {{{x}}} with {{{y}}} and every occurrence of {{{y}}} with {{{x}}}.

{{{x= 6/y-7}}}

3. Solve for {{{y}}} in terms of {{{x}}}.

{{{x= 6/y-7}}}

{{{x + 7= 6/y}}}.........multiply by {{{y}}}

{{{y(x + 7)= 6}}}

{{{y= 6/(x + 7)}}}


4. Replace {{{y}}} with {{{f^-1(x)}}}. 

{{{f^-1(x)= 6/(x + 7)}}}