Answer:
D
Step-by-step explanation:
To find inverse function, we need to follow the steps:
1. Change f(x) to y
2. Interchange x and y
3. solve for new y
4. Change y to [tex]f^{-1}(x)[/tex]
Let's do this with the function given:
[tex]f(x)=\frac{2x+1}{x-4}\\y=\frac{2x+1}{x-4}\\x=\frac{2y+1}{y-4}\\x(y-4)=2y+1\\xy-4x=2y+1\\xy-2y=4x+1\\y(x-2)=4x+1\\y=\frac{4x+1}{x-2}\\f^{-1}(x)=\frac{4x+1}{x-2}[/tex]
To find [tex]f^{-1}(3)[/tex], we plug in 3 into the inverse equation:
[tex]f^{-1}(x)=\frac{4x+1}{x-2}\\f^{-1}(3)=\frac{4(3)+1}{(3)-2}\\f^{-1}(3)=\frac{13}{1}\\f^{-1}(3)=13[/tex]
D is the correct answer.
