1. ## [SOLVED] inverse functions

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?

2. Originally Posted by lonejunior
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.
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