Question 976196
Given: {{{f(x) = (6x-6)/(3x+3) }}}

Find the inverse function, {{{f^-1(x)}}}

since {{{f(x) = y }}}, we have

{{{y= (6x-6)/(3x+3) }}}......swap {{{x}}} and {{{y}}}


{{{x= (6y-6)/(3y+3) }}}


{{{x= cross(6)2(y-1)/cross(3)(y+1) }}}


{{{x= 2(y-1)/(y+1) }}}

{{{x(y+1)= 2(y-1) }}}

{{{xy+x= 2y-2 }}}


{{{x+2= 2y-xy }}}


{{{x+2= (2-x)y }}}


{{{(x+2)/(2-x)=y }}}


{{{y=(x+2)/(2-x) }}}

so, inverse is {{{f^-1(x)=(x+2)/(2-x) }}}