How do you find the inverse of f(x)=x/(x+3)?

1 Answer
Oct 27, 2015

Note that if g(x) is the inverse of f(x)
then f(g(x)) = x
Solve f(g(x)) = g(x)/(g(x)+3) = x for g(x)

Explanation:

Substituting g(x) for x in the original definition of f(x)

f(g(x)) = g(x)/(g(x)+3) = x

g(x) = x*g(x) + x*3

g(x)-g(x)*x = 3x

g(x)(1-x) = 3x

g(x) = (3x)/(1-x)