Question

How do i find the inverse of f(x) = (6x + 3)/(x-8)

Answer 1

F-1(x)=3+8x/x-6 this is the inverse

Answer 2

Answer:   $f^{-1}(x)=\dfrac{8x+3}{x-6}$

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.

$\underline{\text{Given:}}\\y=\dfrac{6x+3}{x-8}\\\\\\\underline{\text{Swap the x's and y's:}}\\x=\dfrac{6y+3}{y-8}\\\\\\\underline{\text{Solve for y:}}\\x(y-8)=6y+3\\\\xy-8x=6y+3\\\\xy-6y=8x+3\\\\y(x-6)=8x+3\\\\\large\boxed{y=\dfrac{8x+3}{x-6}}$