Re: Positive/Negative after taking the square root

On Nov 28, 5:21 pm, matt271829-n...@xxxxxxxxxxx wrote:
On Nov 29, 12:06 am, matt271829-n...@xxxxxxxxxxx wrote:

<snip>

When you substitute u = x^2 you're losing information about which of
the two possible values of x you're dealing with. (This always happens
when the inverse function is multi-valued.)

A simple example of this, which I suppose is vaguely related to the
matter in hand, would be a definite integral between x = -1 and x = 1.
With the substitution u = x^2 this appears to become an integral
between u = (-1)^2 = 1 and u = 1^2 = 1, which is obviously wrong.

Which all goes to show that when one is playing around with
multivalued relationships, one needs to be more careful than
when playing around with functions (single-valued relationships).
.

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