Question 122528
# 15


{{{f(x)=(5x-1)/(2x+3)}}} Start with the given function



{{{x=(5f(x)-1)/(2f(x)+3)}}} Switch the x and f(x) variables. Now the goal is to solve for f(x)



{{{x(2f(x)+3)=5f(x)-1}}} Multiply both sides by {{{2f(x)+3}}} 



{{{2x*f(x)+3x=5f(x)-1}}} Distribute



{{{2x*f(x)+3x-5f(x)=-1}}} Subtract 5f(x) from both sides



{{{2x*f(x)-5f(x)=-1-3x}}} Subtract 3x from both sides



{{{f(x)(2x-5)=-1-3x}}} Factor out f(x) from the left side



{{{f(x)=(-1-3x)/(2x-5)}}} Divide both sides by {{{2x-5}}} to isolate f(x)




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Answer: 


So the inverse function is 


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



So the answer is A)