Question 364470
{{{y=6x-2/x}}}
{{{x=6y-2/y}}}
{{{xy=6y^2-2}}}
{{{6y^2-xy=2}}}
Complete the square in {{{y}}}.
{{{6(y^2-(x/6)y)=2}}}
{{{6(y^2-(x/6)y+(x^2/144))=2+6(x^2/144)}}}
{{{6(y-x/12)^2=2+x^2/24}}}
{{{(y-x/12)^2=1/3+x^2/144}}}
{{{y-x/12=0 +- sqrt(1/3+x^2/144)}}}
{{{y=x/12 +- sqrt(1/3+x^2/144)}}}
{{{highlight(f^(-1)(x)=x/12 +- sqrt(1/3+x^2/144))}}}
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Use the inverse function and substitute {{{x=-1}}} and {{{x=-4}}} and solve for {{{f^(-1)(x)}}}.