Math Help - Solving equations involving inverse function (gf)^-1

1. [SOLVED] Solving equations involving inverse function (gf)^-1

The functions f and g are defined by

f(x) = (1-x)/(2-x), x >2 and
g(x) = xlnx (x more than or equals to 1)

f^-1(x) is (2x-1)(x-1).

Solve exactly the equation (gf)^-1(x) = 3.

What I've got:
gf (x) = ((1-x)/(2-x)) ln ((1-x)/(2-x))
But I can't make x the subject.

Or, (gf)^-1 = f^-1g^-1 . So find g^-1 first and then f^-1.

But I can't find g^-1. I'm stuck.

The answer is x = 2ln2, but I can't seem to get it. Can someone please help me out here? I've been trying for ages. Thanks!

2. $(g\circ f)^{-1}(x)=3\Leftrightarrow x=(g\circ f)(3)$ so, $x=(g\circ f)(3)=\ldots=2\log 2$ .

3. thanks!!

4. Originally Posted by thesocialnetwork
thanks!!

You are welcome!