Question

Can someone explain why |x| = sqrtx^2

Answer 1

\[\sqrt{9} = \pm3\]"sqrt of positive is also always positive" ???

Answer 2

sorry about that

Answer 3

so, anyone???

Answer 4

then the above relation is not true

Answer 5

i mean not absolutely

Answer 6

thats what i think, but someone just said it is, turinTest, i think. And he was preaty sure about it....

Answer 7

can you show me where??

Answer 8

http://openstudy.com/updates/4f6f57e4e4b0772daa0906de?source=email

Answer 9

√9 !=-3 but √9=+3

Answer 10

ya, i just so his explanation, but loks so forced to me. Maybe just my problem

Answer 11

yeah that's right, because he is taking the positive root of x, which is equal to the positive value of x

Answer 12

but x can one value between -ve and +ve, but absolute value of x will always be equal to the positive root of x^2

Answer 13

\[|x|=-x (x<0)\]\[|x| = x (x>0)\]
so, to puting them bouth together he using |x| for root values

Answer 14

root is multivalued function...

Answer 15

to be honest I made silly statement with out a thought.
'root of positive is always positive' ... but i should rather have been 'positive root of ..'

Answer 16

right

Answer 17

When you square a number, you lose the sign. Once it is gone, it doesn't come back. So taking the root of the square is just like taking the absolute value.

Answer 18

he is taking THE POSITIVE ROOT

Answer 19

heheh ... positive root will always be positive and negative root will always be negative. in above case you are also taking the positive root

Answer 20

hmm.. I agree with sign los, but when you take the root you will get +/- anyway

Answer 21

and also -|x| = - sqrtx^2

Answer 22

right

Answer 23

so i guess:\[|x| = \sqrt{x ^{2}}\]
is just the way to write:
\[\pm x = \sqrt{x ^{2}}\]

Answer 24

no ... the second is not right, because on the right hand side ... you have already chosen the positive root

Answer 25

i don't think i chouse anything. x can be negative, can be positive. Same for the sqrt

Answer 26

the EXPRESSION on right hand side must be positive

Answer 27

x2 is >0 no mater what x is

Answer 28

yup, that is if x has real value

Answer 29

sorry, my browser won't let me use the equation applet, but:

(the square root of x) squared is always going to be positive

Answer 30

and why? plz explain

Answer 31

any number squared will be positive, no?

Answer 32

because if x has a real value, then the value of x is either going to be positive or negative .. and the positive multiplication with positive is always positive and -x- is also always postive

Answer 33

if real yes. But continue

Answer 34

But??

Answer 35

I have no imagination. Nor do I understand sarcasm. Sorry.

Answer 36

my point is: you "aplye" srt function to a square of a nummber. Root function gives you two possible values +/-. You don't know what x (+,-) was used to get the square.

Answer 37

the root function doesn't give you two value ... the root function gives you one value ... it's only becuse you have two roots, one negative the other positve

Answer 38

and also be definition of function, function gives you one value ..

Answer 39

there are multivalued functions, and square root is one of them...

Answer 40

arsen another

Answer 41

arcsen*

Answer 42

let me repeat this, a function CANNOT give you two values,

Answer 43

it can and it gives

Answer 44

and arcsin(x) is not a function, if it's range is not defined with in [-pi/2, pi/2]

Answer 45

In mathematics, a function[1] is a correspondence from a set of inputs to a set of outputs that associates each input with exactly one output --- from wikipedia

Answer 46

a function is a set of ordered pairs of one, or two sets. No more restrictions are aplyed

Answer 47

a function maps each value in its domain to one not necessarily unique value of the range

you will not have a function by definition with multiple y-values for one x-value

Answer 48

no .. not exactly, a function must give exactly one output for one or many input // as accessdenied said, unique is not necessary condition ... but it must give one output ... not many outputs

Answer 49

agree about that each value of the domain is mapped. But can be mapped to more than one value in codomain

Answer 50

sqrt of 1 has 2 values. Third root: 3, and so on

Answer 51

nth root has n values

Answer 52

no .. sqrt has one and only one value

X^2 - 1 = 0, x=+-1 are roots of equation on/// not the value of srt 1

Answer 53

sqrt has two values. The positive one is cold principal value, but there is also a negative one.

Answer 54

can you show me in graph???

Answer 55

f(x) = sqrt(x)

Answer 56

http://en.wikipedia.org/wiki/Multivalued_function
look there in examples for multivalued functions. For graphing you need to deside which value will you use, normaly principal is taken

Answer 57

sqrt graph maps positive R to it self, but that principal value of the root

Answer 58

multivalued function and function are different things ... they have different criteria and different things ,, the graph of sqrt x is given here

http://www.wolframalpha.com/input/?i=%28x%29%5E1%2F2

Answer 59

i know the graph, thats not the point of my question

Answer 60

if sqrt x is a multivariable function then it must be something like this