g(x) = 3x+5 / x-1 find the inverse function

I will assume you meant
g(x) = (3x+5)/(x-1)

step 1: interchange the x and y variables

inverse is: x = (3y+5)/(y-1)
step 2: solve this new equation for y
cross-multiply
3y+5 = xy - x
3y - xy = -5-x
y(3-x) = -5-x
y = (-5-x)/(3-x)
or
y = (5+x)/(x-3)

so g^-1 (x) = (5+x)/(x-3)

check with x=2 (or any other value of x)
g(7) = 11/1 = 11
g^-1(11) = 16/8 = 2

thanks man

boo
scary