Re: Simple Quesion making one variable a function of another
- From: magidin@xxxxxxxxxxxxxxxxx (Arturo Magidin)
- Date: Mon, 14 Apr 2008 16:30:29 +0000 (UTC)
In article <fOCdnbLIBsL5GZ7VnZ2dnUVZ8selnZ2d@xxxxxxxxx>,
Jack <notaround@xxxxxxxxxxxx> wrote:
Sorry about this, but its years since I've done this sort of stuff.
How can I reverse this and make x a function of y here:
y=x(x-100)/100
TIA
Technically, you cannot make x a single-valued function of y, since
different values of x will yield the same value of y; for example, x=0
and x=100 will both give y=0, so if you had x = f(y), then f(0) would
have to be both 0 and 100.
On the other hand, you ->can<- make x into a "multi-valued function"
of y.
From y = x(x-100)/100 you get 100y = x(x-100), or x^2 - 100x =100y. Moving the 100y to the left you get
x^2 - 100x - 100y = 0
and now you can use the quadratic formula to get the values of x in
terms of y. You'll get (usually) two values of x for each value of y,
with the exception of y = -25, which produces the single value x=50.
--
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"It's not denial. I'm just very selective about
what I accept as reality."
--- Calvin ("Calvin and Hobbes" by Bill Watterson)
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Arturo Magidin
magidin-at-member-ams-org
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