Question 682489
Inverse function is NOT determined by swapping x and y then solving y, 
it IS determined by solving for x and then swapping the x and y variables.
y = {{{(2x-3)/(x+1)}}} ==> multiply both sides by (x+1)
y(x+1) = (2x-3) ==> distribute the y
xy+y = 2x-3 ==> group x variables on the left
xy + 2x = -3 - y ==> factor out the x variable
x(y+2) = -3 - y ==> divide both sides by (y+2) to isolate x
x = (-3-y)/(y+2) ==> swap x and y variables
{{{f^-1(x) = (-3-x)/(x+2)}}}
...
restriction in f(x) is {{{x+1<>0}}}
{{{x<>-1}}}
restriction in {{{f^-1}}} is {{{x+2<>0}}}
{{{x<>-2}}}
...
domain is all real numbers except -1 and -2
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