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x^2 = y determines a function,

if y^2 = x determines a function,

if y = x^2 determines a function,

and if x = y^2 determines a function.

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- Thread starter Fritz
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- #1

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x^2 = y determines a function,

if y^2 = x determines a function,

if y = x^2 determines a function,

and if x = y^2 determines a function.

- #2

matt grime

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Are we to presume you mean from R to R?

nb those are equalities, you need to say what x and y are.

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In my book it says that y^2 = x does not define a function. Why?

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matt grime

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A function from X to Y is a subset of XxY such that for all x in x there is a unique y in Y such that (x,y) is in this subset. X is the domain Y the codomain.

If we take RxR, and the subset defined by {(x,y) | y=x^2} then this defines a function.

{(x,y) | x=y^2} isn't a function since x=1 has two possible y's, 1 and -1.

You book assumes some intrinsic meaning for x and y, it appears, that we don't all share.

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jcsd

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jcsd

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Is y always the output and x the input?

You can have y = x^2 but not x = y^2. Is this because y is always the range and x the domain?

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matt grime said:

A function from X to Y is a subset of XxY such that for all x in x there is a unique y in Y such that (x,y) is in this subset. X is the domain Y the codomain.

If we take RxR, and the subset defined by {(x,y) | y=x^2} then this defines a function.

{(x,y) | x=y^2} isn't a function since x=1 has two possible y's, 1 and -1.

You book assumes some intrinsic meaning for x and y, it appears, that we don't all share.

I don't understand any of this!

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jcsd

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Fritz said:

Is y always the output and x the input?

You can have y = x^2 but not x = y^2. Is this because y is always the range and x the domain?

If you don't know/can't find out what the domain or the range is then you don't know what the function is! The range and thedomian is part of the function.

By convention 'x' usually denotes 'a member' of the domain and 'y' denotes 'a member' of the range (or of the image set if you prefer).

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matt grime

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dav2008

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If

Consider y=x

However, look at the same equation of y=x

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JasonRox

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y^2=x can be a function depending on how you want to look at it. For now, let's say it is not. I understand where your textbook is going, but I don't think they should do that.

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matt grime

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dav2008

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We're also pretending that he's not doing graduate work for a mathematics degree.matt grime said:

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jcsd

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dav2008 said:We're also pretending that he's not doing graduate work for a mathematics degree.

Functions which do not have R as the domain are common throughout math, for example sequences represent functions with N as the domain and functions with complex domains are very important to both to mathematicans and physicists. The only way to know if a 'function' is infact a function is to look at the primitive concept.

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matt grime

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Just because at a lower level the 'correct' definitions (if such a thing can be said to exist) aren't used doesn't mean that when someone has a question that requires them we should not use them.

Just saying is x^2=y a function doesn't mean anything: is what a function of what on what domain (and hence range/codomain)? These are all necessary to answer the question at any level. Functions properly arise in the first year of an *under*graduate course in the UK.

And this is important in say taking square roots, where we don't even need to go outside the real numbers. y=sqrt(x) does not define a function from R to R (x is in the domain), but it is a function from R+ (the positive reals) to R.

Just saying is x^2=y a function doesn't mean anything: is what a function of what on what domain (and hence range/codomain)? These are all necessary to answer the question at any level. Functions properly arise in the first year of an *under*graduate course in the UK.

And this is important in say taking square roots, where we don't even need to go outside the real numbers. y=sqrt(x) does not define a function from R to R (x is in the domain), but it is a function from R+ (the positive reals) to R.

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- #17

matt grime

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A function, f, is an unambiguous way of assigning to each element in D (the domain) an element in C (the image set)

Note, the domain, aka preimage, and image set are part of the definition still. You can't get round that fact as hopefully the example of sqrt( ) demonstrates without going beyond anyone's knowledge.

- #18

JasonRox

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y=sqrt(x), then we always take the positive so we can create a function out of it.

The only time you take both is when y=+-sqrt(x), which implies y^2=x and this not a function. Under this assumption y=-sqrt(x) implies that we only take the negative value and makes this a function.

I don't know if the UK goes by this convention, but I think its important to know or they make it important to know.

Personally, if you don't understand what a function is, then how will you get through the inverse functions? They generally have the same meaning, but if you can't understand the first you obviously don't understand the second.

Note: I'm just blabbing on. I just thought you'd like to know the basic convention here in North America.

- #19

matt grime

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Erm, jason, the "convention" is that of mathematics, and in this case is universal.

y^2=x will not define y as a function of x in general though you are making the same mistake as everyone else by not specifying the domain (and codomain).

So, what do you mean by is or isn't a function if you do not state from where to where!

y=sqrt(x) even with the single valued choice of the root does not define a function from R to R, again x as the input since there is no real number that is the square root of a negative real number.

y=sqrt(x) from R+ to R is function since we always take it to mean the principal branch.

y^2=x will not define y as a function of x in general though you are making the same mistake as everyone else by not specifying the domain (and codomain).

So, what do you mean by is or isn't a function if you do not state from where to where!

y=sqrt(x) even with the single valued choice of the root does not define a function from R to R, again x as the input since there is no real number that is the square root of a negative real number.

y=sqrt(x) from R+ to R is function since we always take it to mean the principal branch.

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E=mc2 is the velocity of 5 x r3 to the exponent 5 i understand the symbols but cant get the grasp of putting it as one please help E=mc2 is the velocity of 5 x r3 to the exponent 5

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HallsofIvy

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zim777 said:E=mc2 is the velocity of 5 x r3 to the exponent 5 i understand the symbols but cant get the grasp of putting it as one please help E=mc2 is the velocity of 5 x r3 to the exponent 5

This makes absolutely no sense! "E= mc2" is an equation, it can't be a velocity of anything.

In any case, only objects have "velocity". "4 x r3 to the exponent 5" (by which I assume you mean (4r

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Poor Fritz.

He's probably just trying to pass a high school course for crying out loud.

He's probably just trying to pass a high school course for crying out loud.

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JasonRox

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I do know what domains, and it is very important to know what it is. Same with the range.

All I was saying is that the convention is to avoid confusion between what is a function and what is not.

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