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

1 Answer
Oct 27, 2015

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

Explanation:

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

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

g(x) = x*g(x) + x*3g(x)=xg(x)+x3

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

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

g(x) = (3x)/(1-x)g(x)=3x1x