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How can I build a function f(x) such that $5 < f(x) < 10$?

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closed as not a real question by Gerry Myerson, sdcvvc, Zhen Lin, Henning Makholm, Asaf Karagila Sep 3 '12 at 13:27

It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, visit the help center.If this question can be reworded to fit the rules in the help center, please edit the question.

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Will $f(x) = 4$ do? –  quanta Apr 30 '11 at 5:15
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What have you tried? Why do you want to do this? –  JavaMan Apr 30 '11 at 5:15
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What exactly are you planning to do with such a function? –  J. M. Apr 30 '11 at 5:16
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$f(x)=\sin x+5$ is another option. –  yunone Apr 30 '11 at 5:18
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This should be closed-easily too localized and useless. –  picakhu Apr 30 '11 at 5:21

1 Answer 1

up vote 5 down vote accepted

I figured I would come up with 5 examples (why 5? because it is prime, it is a congruent number, it represents a chevron in its Roman numeral and is therefore incredibly masculine if we believe Dan Brown at all, and leads to the beautiful self-referential sentence: "In this exclamation, there are five i's!"

  1. $f(x) = 5$. This is not a very exciting one, but we get more exciting later.
  2. $f(x) = |x| + 5$. This is about as exciting as the last one, except that it is a bit more pointy. It happens.
  3. $f(x) = x^4 + x^2 + 2 \pi$. One might ask why a $\pi$ appears in this function, and I might respond to that by noting that this is a very reasonable question.
  4. $f(x) = \dfrac{2}{|x|} + 5|cos(x)|+ 5|sin(x)| + 3$. Now we're getting more exciting.
  5. $f(x) = \dfrac{4x^2 + 5}{x^2 + 1}$. This is the so-called Witch of Agnesi function, which is remarkable in many ways. It's limit is 4 for both positive and negative x, but it is always greater than 4! In addition, the phrase "Witch of Agnesi" has 5 vowels.

To complete this little game, I note also that the word "subcontinental" has all five vowels, and they appear in reverse-alphabetic order ("uoiea"). Good day!

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Firstly, I should note that there is no function that satisfies $10 < f(x) < 5$, as $10>5$. Secondly, I should note that that edit occurred after the original post of the question. Thirdly, if you want a number between 5 and 10, you should write $5 < f(x) < 10$ in your description. Fourthly, you should also change your title so that it doesn't read "Math function return value greater than or equal to 4." Fifthly, you should explain why this is a valid question to appease the many people who certainly have their doubts right around now. Unoriental has the same property as subcontinental. –  mixedmath Apr 30 '11 at 5:41
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Teeny nitpick: your #5 technically isn't a witch; a witch is bell-shaped, and takes the form $\frac{\text{constant}}{x^2+\text{constant}}$. –  J. M. May 1 '11 at 22:07
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@J.M.: Well, it's a witch + 4 (which isn't a witch either, but instead one on a broom four units above the plains of MathExchange). –  mixedmath May 1 '11 at 23:39

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