ANSWER
D. 13
EXPLANATION
The given function is:
[tex]f(x) = \frac{2x + 1}{x -4} [/tex]
Let
[tex]y = \frac{2x + 1}{x -4} [/tex]
Interchange x and y.
[tex]x= \frac{2y + 1}{y-4} [/tex]
Solve for y.
[tex]x(y - 4)=2y + 1[/tex]
[tex]xy - 4x=2y + 1[/tex]
[tex]xy - 2y = 1 + 4x[/tex]
[tex](x - 2)y = 1 + 4x[/tex]
[tex]y = \frac{1 + 4x}{x - 2} [/tex]
[tex] {f}^{ - 1}(x) = \frac{1 + 4x}{x - 2} [/tex]
We put x=3,
[tex]{f}^{ - 1}(3) = \frac{1 + 4 \times 3}{3- 2}[/tex]
[tex]{f}^{ - 1}(3) = \frac{13}{1} = 13[/tex]
