SOLUTION: Can you have a function if the answer includes a sq root? for example y= sqrt (x-3) Doesn't this answer include both negative and positive because of the sqrt? Can you explain
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Question 1068968: Can you have a function if the answer includes a sq root? for example y= sqrt (x-3) Doesn't this answer include both negative and positive because of the sqrt? Can you explain why? Thanks. Found 2 solutions by rothauserc, ikleyn:Answer by rothauserc(4718) (Show Source):
You can put this solution on YOUR website! A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output
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Consider the ordered pair (x, y) where x is an element in the set X and y is an element in y such that f(x) = y, f is a function then there can be only one ordered pair with the same value of x.
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We exclude negative values for x, since square root of negative number is an imaginary number
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For any non-negative real number x, there is one and only one non-negative real number s^2 such that s^2=x. (For example: If x=16, then s=4.) This is called the principal square root of x.
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y = sqrt (x-3) is a function for all x > or = 3
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When in the school math we consider the functions like these , , and so on,
the DEFAUL AGREEMENT is in force (in action) that we consider only positive values of the function.
If the opposite is not said directly and explicitly.
In the SAME TIME, if you consider or solve the equation = 16, you must take both values +/-4 and both roots +/-4.
It is ANOTHER AGREEMENT for this ANOTHER specific situation.
So, for each situation ITS OWN AGREEMENT is in force/(in action).
As a rule, in the school math these agreements never prononciate explicitly.
Nevertheless, they ARE in place, they DO act and they ARE in common use.
