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Feb 7th, 2003, 04:15 PM
#1
Fanatic Member
here we go again...
NO! sqrt(X) has only ONE AND ONLY ONE ANSWER! because sqrt(x) is defined to be a function!!! functions, by definition, gives you one and only one! sqrt(x) is in fact "the principle sqrt" which means the non-negative (because it can be 0) square root of a number! its just like sin^(-1)(0) (aka arcsin(9)) that means x=0. sin^(-1)(0) does NOT RETURN INFINITE ANSWERS, although sin(0)=sin(pi)=sin(2pi)=...=0!!
but on the other hand, if you are asked to solve x^2=25, you would then get x=5 and -5, as seen by x^2-25=0 and (x+5)(x-5)=0
because some functions (ie x^2, sin(X)) are not one-to-one, we restrict the domain of the inverse function so the inverse will be actually a "inverse function", ie by definition only RETURNS ONE SINGLE VALUE.
the next time you say sqrt(25) (or 25^(1/2) ) is 5 and -5, first answer this question, what is sin^(-1)(0)??
Massey RuleZ! ^-^__  Cheers!  __^-^ Massey RuleZ!
Did you know that...
The probability that a random rational number has an even denominator is 1/3 (Salamin and Gosper 1972)? This result is independently verified by me (2002)!
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