Period of non trigonometric functions

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Discussion Overview

The discussion revolves around the methods for determining the period of non-trigonometric functions. Participants explore the implications of using the equation f(x+t)=f(x) to find a period t, questioning the conditions under which this approach is valid.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant inquires about a definitive method for finding the period of non-trigonometric functions using the equation f(x+t)=f(x).
  • Another participant asserts that if the equation holds for all x, then the function is periodic with period t, suggesting that solving for t is valid.
  • A subsequent reply questions the validity of obtaining t in terms of x, expressing confusion about how this relates to determining the function's period.
  • Another participant argues against the approach, emphasizing the need for a specific form of the equation that clearly defines t as a non-zero constant to establish periodicity.
  • A humorous remark is made about conserving question marks, highlighting a light-hearted aspect of the discussion.

Areas of Agreement / Disagreement

Participants express differing views on the validity of using the equation f(x+t)=f(x) to find the period of non-trigonometric functions, indicating that the discussion remains unresolved with multiple competing perspectives.

Contextual Notes

There are limitations regarding the assumptions made about the functions in question and the definitions of periodicity that are not fully explored in the discussion.

phymatter
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is there any definite way of finding the period of non trigonometric functions?

can we use f(x+t)=f(x) and solve for t from this equation?
 
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Most functions are not periodic. If the above equation holds for all x then f is periodic with period t. So yes solve for t.
 
deluks917 said:
Most functions are not periodic. If the above equation holds for all x then f is periodic with period t. So yes solve for t.

but when we do so , we get t in terms of x ,so how does this give the period of the function?
 
You shouldn't, no. You want something of the form [tex]\forall x,\ f(x)=f(x+\text{foo})[/tex] where the string of symbols that make up foo are t. Of course you also need that t is not zero to call it periodic, so if the string of symbols was "x-x" then you haven't shown what you wanted to show.

Also please conserve question marks; some children in <insert third-world country> can't afford more than one a day and it looks bad to be so wasteful.
 

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