Consider the following function Find the inverse function of

Consider the following function. Find the inverse function of f.

f(x) = (x+1)/(x-3)

y = (x+1)/(x-3)

f(x) is not deifined for x=3 as denominator becomes zero

So, Domain (-inf , 3) U (3, inf)

Range : f(x) has horizontal asymtote at y=1

So, range (-inf, 1) U (1, inf)

f^-1(x) : plug x = y and y =x

x= (y+1)/(y -3)

xy -3x = y +1

y(x-1) = 1+3x

y = (1+3x)/(x-1)

f^-1(x) = (1+3x)/(x-1)

f^-1(x) does not exist for x=1 as den. becomes zero

So, Domain (-inf, 1) U (1, inf)

Range : f^-1(x) has horizontal asymtote at y =3

So, range (-inf , 3)U (3, inf)