The inverse funtion of
[tex]f(x)=\frac{2x+1}{x-4}[/tex]is
[tex]f^{-1}(x)=\frac{4x+1}{x-2}[/tex]We can check this by doing
[tex]f(f^{-1}(x))=\frac{2(\frac{4x+1}{x-2})+1}{\frac{4x+1}{x-2}-4}=\frac{\frac{8x+2+x-2}{x-2}}{\frac{4x+1-4x+8}{x-2}}=\frac{9x}{9}=x[/tex]Now that we've confirmed it is the inverse function, we simply evaluate at x=3:
[tex]f^{-1}(3)=\frac{4(3)+1}{3-2}=\frac{12+1}{1}=13[/tex]Thus the answer is D.
