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find the domain of the function defined by the following equation :
f (x) = sqrt(x + 6)
x + 6 > 0

subtract 6 both sides
x < 6

(00,6) < is the domain of F
?
Desi
Raat Key Rani !
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the domain of a function f(x), is the range of x for which the function is valid.
since f(x) = sqrt(x+ 6), you are right in that x + 6 >= 0
so you have that x >= 6. (not <)
and that is youre domain, x >= 6.
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The End Of All Things To Come.
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Alternatively, it could be that the domain is only 6, because values of x higher than that give 2 results, meaning the function isn't welldefined.
Why did the vector cross the road?
It wanted to be normal.
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Correct, mathsy. A function should give a single value for a single input, never a "this OR that" answer.
I guess it depends on what level is being taught. When students are first taught "square root" thay are only taught the positive root, so we should really have a function "psqrt" or something that doesn't suffer from the tworesult problem.
So if it is only the positive root then x≥6 is right, otherwise only 6 is valid.
"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman
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I thought that whenever the square root sign is written, as in a function definition for example, it means "extract the positive root"... at least it is like that in all the textbooks i've seen. I have never seen any instance where a function definition involving a square root operator was supposed to mean both possible roots.
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The square root of x is a number that, when squared, gives x. So, the square root of 9 is +3 or 3.
I believe that the use of the radical sign √ refers only to the positive root, so you could say:
√9=+3 and √9=3
But in most mathematics educations the negative root is not dealt with until much later. But once you learn about it, it tends to stick!
"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman
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The square root of x is a number that, when squared, gives x. So, the square root of 9 is +3 or 3.
I believe what is typically called the "square root sign" is actually the principal square root sign.
But in most mathematics educations the negative root is not dealt with until much later. But once you learn about it, it tends to stick!
It's not so much us not dealing with something more complex than it is us wanting everything to be a function.
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."
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