# Function Question

**URL:** <https://boards.straightdope.com/t/function-question/687281>\
**Category:** Factual Questions\
**Created:** [April 29, 2014, 3:19pm UTC](https://boards.straightdope.com/t/function-question/687281 "2014-04-29T15:19:21Z")\
**Posts on this page:** 7\
**Page:** 1

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**Author:** ![drewtwo99](https://avatars.discourse-cdn.com/v4/letter/d/d07c76/32.png) [@drewtwo99](https://boards.straightdope.com/u/drewtwo99)\
**Post date:** [April 29, 2014, 3:19pm UTC](https://boards.straightdope.com/t/function-question/687281/1 "2014-04-29T15:19:21Z")

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I should really be able to do this on my own but I need help with the following problem.

F (x)= D  
F (2x)= D + 3  
F (4x) = D + 6  
…

I need the inverse function G(D+A)=Bx so that if I know D and A I can calculate B.

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**Author:** ![ZenBeam](https://avatars.discourse-cdn.com/v4/letter/z/3ab097/32.png) [@ZenBeam](https://boards.straightdope.com/u/ZenBeam)\
**Post date:** [April 29, 2014, 3:26pm UTC](https://boards.straightdope.com/t/function-question/687281/2 "2014-04-29T15:26:54Z")

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What you wrote doesn’t really make sense.

In general you have

F(x \* 2^N) = D + 3\*N

but assuming D is a constant, how does the right hand side depend on x?

ETA: Maybe you shouldn’t have the X there at all. Does this fit with what you’re trying to do?

F (1)= D  
F (2)= D + 3  
F (4) = D + 6  
…  
F(2^N) = D + 3\*N

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**Author:** ![ZenBeam](https://avatars.discourse-cdn.com/v4/letter/z/3ab097/32.png) [@ZenBeam](https://boards.straightdope.com/u/ZenBeam)\
**Post date:** [April 29, 2014, 3:30pm UTC](https://boards.straightdope.com/t/function-question/687281/3 "2014-04-29T15:30:55Z")

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Then in general, you’d have  
F(X) = D + 3 \* log[sub]2/sub

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**Author:** ![drewtwo99](https://avatars.discourse-cdn.com/v4/letter/d/d07c76/32.png) [@drewtwo99](https://boards.straightdope.com/u/drewtwo99)\
**Post date:** [April 29, 2014, 3:31pm UTC](https://boards.straightdope.com/t/function-question/687281/4 "2014-04-29T15:31:23Z")

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D is not constant

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**Author:** ![Buck\_Godot](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/buck_godot/32/6573_2.png) [@Buck\_Godot](https://boards.straightdope.com/u/Buck_Godot)\
**Post date:** [April 29, 2014, 4:13pm UTC](https://boards.straightdope.com/t/function-question/687281/5 "2014-04-29T16:13:58Z")

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OK so what it sounds like you really want is a function F such that for all x,

F(2x)=F(x)+3

This is clearly impossible for x=0, since it would require that

F(0)=F(0)+3.

However, if we eliminate this point, and we set for X not equal to 0

F(x)=3_log[sub]2/sub=3_log(|x|)/log(2)

we find that

F(2x)= 3_log(|2x|)/log(2) = 3_(log(2)+log(|x|))/log(2) = 3+3\*log(|x|)/log(2) = 3+F(x)

we have a solution.

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**Author:** ![Buck\_Godot](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/buck_godot/32/6573_2.png) [@Buck\_Godot](https://boards.straightdope.com/u/Buck_Godot)\
**Post date:** [April 29, 2014, 4:22pm UTC](https://boards.straightdope.com/t/function-question/687281/6 "2014-04-29T16:22:57Z")

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PS: you can also add any constant to the above solution and it still works.

So the full set of solutions is of the form

F(x)=3\*log[sub]2/sub+C for any constant C and x not equal to 0. Basically what ZenBeam said.

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**Author:** ![drewtwo99](https://avatars.discourse-cdn.com/v4/letter/d/d07c76/32.png) [@drewtwo99](https://boards.straightdope.com/u/drewtwo99)\
**Post date:** [April 30, 2014, 2:29am UTC](https://boards.straightdope.com/t/function-question/687281/7 "2014-04-30T02:29:13Z")

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Thanks for the help guys!