[tex]f^{-1}[/tex](x) = - [tex]\frac{4+x}{2x-6}[/tex]
let y = [tex]\frac{6x-4}{2x+1}[/tex]
rearrange making x the subject, begin by cross-multiplying
y(2x + 1) = 6x - 4
2xy + y = 6x - 4
collect terms in x together
2xy - 6x = - 4 - y
x(2y - 6) = - (4 + y ) ( divide both sides by (2y - 6) )
x = [tex]\frac{-(4+y)}{2y-6}[/tex]
change y back to x for inverse
[tex]f^{-1}[/tex](x) = - [tex]\frac{4+x}{2x-6}[/tex]
