Re: How Do I Invert These Two Functions
- From: quasi <quasi@xxxxxxxx>
- Date: Wed, 28 Nov 2007 18:47:41 -0500
On Wed, 28 Nov 2007 18:35:14 -0500, quasi <quasi@xxxxxxxx> wrote:
On Wed, 28 Nov 2007 23:23:02 GMT, John Schutkeker
<jschutkeker@xxxxxxxxxxxxxxxxxxxx> wrote:
If I define u1(r1,r2)=(1/r1)+(1/r2) and u2(r1,r2)=1/(r2-r1). How would I
go about solving these two equations for r1(u1,u2) and r2(u1,u2), which
would constitute "inverting the functions"? Thanks In Advance!
Elementary algebra! Try it before giving up.
Write down 2 equations:
u1 = (1/r1)+(1/r2)
u2 = 1/(r2-r1)
Viewing r1,r2 as the unknowns, you have 2 equations in 2 unknowns.
How hard can it be?
Of course, there are always tricks, but before looking for tricks, how
about trying the most basic method (from elementary algebra):
Choose one equation and solve that equation for one of the unknowns in
terms of the other. Then use the result as a replacement for that
unknown in the other equation, thus yielding one equation in one
unknown. You should be able to figure out the rest.
You try it.
Also, for a function to be invertible, it has to be one-to-one. But as
you'll see when you solve algebraically, your function is mostly
two-to-one (on R^2).
quasi
.
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