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hi guys, what is the relationship between y^2 = f(x) and y = f(x)?

thank you.

thank you.

- Thread starter mune
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- #1

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hi guys, what is the relationship between y^2 = f(x) and y = f(x)?

thank you.

thank you.

- #2

symbolipoint

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- #3

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Or y=0...

/*extra characters*/

- #4

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for example, if y=f(x) have a maximum point at (a,b), will y^2=f(x) have a maximum point at(a,b) too?

i hope i make my question clear.

- #5

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it is not a trick question, nor a very highly theoretical question.

- #6

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Oh, you don't really mean y=f(x), and y

for example, if y=f(x) have a maximum point at (a,b), will y^2=f(x) have a maximum point at(a,b) too?

i hope i make my question clear.

so lets let

y=f(x) and

z=(f(x))

Obviously z is always positive assuming we are only dealing with real numbers, but to investigate a relation about maxima/minima lets look at y'.

y'=f'(x) and

z'=2f(x)f'(x)

if f(x) has a max/min at the point (a,b) then f'(a)=0

Then y'(a)=0, and I think you can see then that z'(a)=2f(a)f'(a), but f'(a)=0 so z'(a)=0, thus the function z or (f(x))

I think it should be fairly easy to show that if f has a min at x=a then so does f

- #7

HallsofIvy

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Let's clarify by taking f(x)= x. What is the relationship between y= x and y

Suppose f(x)= x+ 3. What is the relationship between y= x+ 3 and y

Frankly, I don't see much relationship. The first is a function and the second, for general f(x), is NOT a function. The first

- #8

Gib Z

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thank you everyone

sorry that I didn't explain my question clearly. Anyway, Gib Z and HallsofIvy know what I mean

but thanks d_leet too, I have learnt a way to prove from your post.

sorry that I didn't explain my question clearly. Anyway, Gib Z and HallsofIvy know what I mean

but thanks d_leet too, I have learnt a way to prove from your post.

Last edited:

- #10

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That depends on whether f(a) is positive or negative. If f(a) is negative and a minimum, (f(a))^2 may be a maximum (e.g., if f(x) is the cosine function, then f(pi) is a minimum put (f(pi))^2 is a maximum).I think it should be fairly easy to show that if f has a min at x=a then so does f^{2}, and the same if f has a max at x=a, but I'm a bit too tired to try a proof of that at the moment.

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