Period of non trigonometric functions

[phymatter]

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?

 

[deluks917]

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.

 

[phymatter]

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?

 

[CRGreathouse]

You shouldn't, no. You want something of the form $$\forall x,\ f(x)=f(x+\text{foo})$$ 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.

 

[CellCoree]

I can say that there is no definite way of finding the period of non-trigonometric functions. Unlike trigonometric functions, which have a clear and consistent pattern of repetition, non-trigonometric functions can have varying patterns and behaviors. Therefore, it is not possible to determine the period of a non-trigonometric function without specific information about the function itself.

Using the equation f(x+t)=f(x) to solve for t may provide some information, but it is not a guaranteed method for finding the period. It may work for some functions, but not for others. Additionally, it may only provide an approximate value for the period, rather than an exact solution.

In order to determine the period of a non-trigonometric function, it is necessary to analyze its graph or mathematical representation and look for patterns or repetitions. This may involve using calculus techniques, such as finding the derivative or integral of the function, or using algebraic methods to manipulate the equation and identify any repeating terms.

In conclusion, while there is no definite way to find the period of non-trigonometric functions, there are various methods and techniques that can be used to approximate or determine the period depending on the specific function being analyzed.