so i'm really lost with inverses..
can someone just explain to me how to do it?
g(x)= 1-1/(x-1)
and
g^-1(x)= 1+1/(1-x)
how do you prove that they are or are not inverses?
I've lost track of how many times I've said this, but: by showing that the definition holds.
The definition of "inverse function" is:
$\displaystyle g^{-1}$ is the inverse function to g(x) if and only if $\displaystyle g^{-1}(g(x))= x$ and $\displaystyle g(g^{-1}(x))= x$.
If g(x)= 1- 1/(x-1) and $\displaystyle g^{-1}(x)= 1+ 1/(1- x)$, then [tex]g^{-1}(g(x))= g^{-1}(1- 1/(x-1))= 1+ 1/(1-[1-1/(x-1)]). Show that that is equal to x and the do it the other way.