Question 1015206


{{{g(x)=(x+5)/(x+2)}}}, to find the inverse function {{{g^-1(x)}}}, first replace {{{g(x)}}} with {{{y}}}

{{{y=(x+5)/(x+2)}}}.....now swap {{{x}}} and {{{y}}}

{{{x=(y+5)/(y+2)}}}....solve for {{{y}}}

{{{x(y+2)=(y+5)}}}

{{{xy+2x=y+5}}}

{{{xy-y=5-2x}}}

{{{y=(5-2x)/(x-1)}}}

so, {{{g^-1(x)=(5-2x)/(x-1)}}}