Re: determining if function has inverse

In article <1183950065.084352.223450@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
conrad <conrad@xxxxxxxxxx> wrote:

Is there a way to determine if
a function has an inverse?

I'm trying to find the inverse of
[(x - 3)(x + 3)] / [(2x + 3)(x - 5)]

And I've managed to get up to:
y^2 = x(2y^2 - 7y) - 6

At which point it seems impossible
to isolate y. Any help appreciated.

--
conrad

In order to have an inverse function, it must be one-to onefrom its
domain to its range.

Thus the equation y = [(x - 3)(x + 3)] / [(2x + 3)(x - 5)]
must have a unique solution in x for each value of y for which it has
any solution in x.

But y = 0 gives x = 3 and x = -3 as non-unique corresponding solutions.
.