Inverse function

Question

find the inverse of g(x)=(x-4)/(x-2)

Answer 1

g(x) = (x - 4) / (x - 2)

x = (g^-1(x) - 4) / (g^-1(x) - 2)     form inverse

x(g^-1(x) - 2) = g^-1(x) - 4           multiply both sides by denominator

xg^-1(x) - 2x = g^-1(x) - 4            distribute

xg^-1(x) = g^-1(x) + 2x - 4          add 2x to both sides

xg^-1(x) - g^-1(x) = 2x - 4           subtract g^-1(x) from both sides

g^-1(x)(x - 1) = 2x - 4               factor

g^-1(x) = (2x - 4) / (x - 1)