Question 121733
#1


{{{f(x)=(3x-5)/(x+2)}}} Start with the given function



{{{x=(3f(x)-5)/(f(x)+2)}}} In order to find the inverse function, replace every x with f(x) and vice versa.


So the goal is to solve for f(x)



{{{x(f(x)+2)=3f(x)-5}}} Multiply both sides by {{{f(x)+2}}}



{{{xf(x)+2x=3f(x)-5}}} Distribute



{{{xf(x)+2x-3f(x)=-5}}} Subtract 3f(x) from both sides



{{{xf(x)-3f(x)=-5-2x}}} Subtract 2x from both sides



{{{xf(x)-3f(x)=-2x-5}}} Rearrange the terms



{{{f(x)(x-3)=-2x-5}}} Factor out f(x)



{{{f(x)=(-2x-5)/(x-3)}}} Divide both sides by {{{x-3}}} to isolate f(x)




----------------------


So the inverse function is 



{{{f^(-1)(x)=(-2x-5)/(x-3)}}} 





So the answer is B)