Question

find inverse f(x) = 3x/(x-6)

Answer 1

take f(x)=y
y=3x/(x-6)
y(3x-6)=3x
3xy-6y=3x
3xy-3x=6y
x=2y/(y-1)

Answer 2

also note that f(6) is undefined

Answer 3

it is saying the answer is incorrect

Answer 4

write it as \[y = \frac{3x}{x - 6}\] and the domain restriction is \[x \neq 6\] swap x and y \[x = \frac{3y}{y - 6}\] now make y the subject of the equation.

Answer 5

multiply both sides by y - 6 \[x(y - 6) = 3y\] distribute \[xy - 6x = 3y\] subtract xy from both sides of the equation \[-6x = 3y - xy\] factor the left hand side

\[-6x = y(3 - x)\]

I'll leave you to finish it off..