Answer: [tex]f^{-1}(x)=\dfrac{8x+3}{x-6}[/tex]
Step-by-step explanation:
To find the inverse, swap the x's and y's and solve for y. Note that f(x) is y.
[tex]\underline{\text{Given:}}\\y=\dfrac{6x+3}{x-8}\\\\\\\underline{\text{Swap the x's and y's:}}\\x=\dfrac{6y+3}{y-8}\\\\\\\underline{\text{Solve for y:}}\\x(y-8)=6y+3\\\\xy-8x=6y+3\\\\xy-6y=8x+3\\\\y(x-6)=8x+3\\\\\large\boxed{y=\dfrac{8x+3}{x-6}}[/tex]
