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MJ_23
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I've got a question asking to find the range of f for the function below

f: x |-> x^2 -2x + 3 , x e R, 0 <= x <= 4

I sub in x for 4 and get 11, but don't know where to go from there.
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TheWolf
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#2
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(Original post by MJ_23)
I've got a question asking to find the range of f for the function below

f: x |-> x^2 -2x + 3 , x e R, 0 <= x <= 4

I sub in x for 4 and get 11, but don't know where to go from there.
why not draw the graph, and find the minimum point?
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Bezza
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(Original post by MJ_23)
I've got a question asking to find the range of f for the function below

f: x |-> x^2 -2x + 3 , x e R, 0 <= x <= 4

I sub in x for 4 and get 11, but don't know where to go from there.
Complete the square, f(x) = (x-1)^2 + 2
(x-1)^2 > 0 for all x so f(x)>2
min pt is (1,2) so range is f(x)>2
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IntegralAnomaly
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(Original post by MJ_23)
I've got a question asking to find the range of f for the function below

f: x |-> x^2 -2x + 3 , x e R, 0 <= x <= 4

I sub in x for 4 and get 11, but don't know where to go from there.
complete the square to get f(x)=(x-1)²+2.
so the minimum point is when x=1,and f(x)=2.
Or u can find f': f'(x)=2x-2.At minimum f'(x)=0 therefore x=1 so f(x)=2.
Since f(x) must lie above or on this minimum point the range is f(x)≥2
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Fermat
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max value for f is when x = 4
f(x=4) = 4² - 2.4 + 3
f_max = 11

therefore range of f is
2 <= f <= 11
=========
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IntegralAnomaly
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(Original post by Fermat)
max value for f is when x = 4
f(x=4) = 4² - 2.4 + 3
f_max = 11

therefore range of f is
2 <= f <= 11
=========
are u sure?:
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Fermat
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(Original post by IntegralAnomaly)
are u sure?:
Yep.
the range, or domain, of x is given as
0 <= x <= 4

That means that x cannot take a value less than 0 or greater than 4, so must be constrained to lie within the lines x=0 and x=4.
The minimum of the curve gives the lower end of the range of f, i.e. f=2.
Since the value of x cannot exceed 4 then max f is given by f(x=4) = 11.
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IntegralAnomaly
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(Original post by Fermat)
Yep.
the range, or domain, of x is given as
0 <= x <= 4

That means that x cannot take a value less than 0 or greater than 4, so must be constrained to lie within the lines x=0 and x=4.
The minimum of the curve gives the lower end of the range of f, i.e. f=2.
Since the value of x cannot exceed 4 then max f is given by f(x=4) = 11.
Oops,i didn't see that bit!sorry
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Fermat
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(Original post by IntegralAnomaly)
Oops,i didn't see that bit!sorry
no prob
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IntegralAnomaly
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(Original post by Fermat)
no prob
sorry fermat but you posted 2 sites about latex a while ago,what was the other one?(not the one u pm me).
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Bhaal85
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What's latex?
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IntegralAnomaly
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(Original post by Bhaal85)
What's latex?
have u heard of mathtype?this is ten times better:http://www.latex-project.org/.
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Bhaal85
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(Original post by IntegralAnomaly)
have u heard of mathtype?this is ten times better:http://www.latex-project.org/.
Confused by it all, which is the one I need to be able to use mathematical signs, I'm on WinXP, which do I download?
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Silly Sally
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(Original post by IntegralAnomaly)
sorry fermat but you posted 2 sites about latex a while ago,what was the other one?(not the one u pm me).
When i first read this post, i thought you were talking about latex material (as in gloves) and i thought that was VERY random!!! Now i just feel stupid
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Bhaal85
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(Original post by Silly Sally)
When i first read this post, i thought you were talking about latex material (as in gloves) and i thought that was VERY random!!! Now i just feel stupid
How silly. lol (If its any consolation, I too thought that when it was first mentioned weeks before).
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IntegralAnomaly
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(Original post by Bhaal85)
Confused by it all, which is the one I need to be able to use mathematical signs, I'm on WinXP, which do I download?
i recommend u start using latex after ur exams finish because it is useful at uni,assuming that ur doin a science based degree.Here's an example of how it looks:http://mathworld.wolfram.com/GammaFunction.html.While mathtype is crap.
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Fermat
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(Original post by IntegralAnomaly)
sorry fermat but you posted 2 sites about latex a while ago,what was the other one?(not the one u pm me).
I've got three sites I've used:
Beginning Latex
Getting Started with LaTeX
LaTeX Tutorial

The last one is mainly for instructing unix users in setting up and runnnng latex on a Unix system but has somwe useful latex info as well.

enjoy!
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Fermat
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#18
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(Original post by Bhaal85)
Confused by it all, which is the one I need to be able to use mathematical signs, I'm on WinXP, which do I download?
To set up a simple latex system, goto http://www.miktex.org and click on the [setup] link to download the small MikTex compiler. Just run the exe file and it will install the package.
Like mikesgt2, I use an editor called TeXnicCenter, which makes editing and compiling documents easier, you can find it here: http://www.texniccenter.org (look for the Download link in the panel on the left)
When you install this, you will be asked for a file viewer (for the dvi files), click on the Browse button, and navigate to C:\texmf\miktex\bin and select yap.exe.
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