# Period of non trigonometric functions

• phymatter
In summary, the conversation discusses the possibility of finding the period of non-trigonometric functions by using the equation f(x+t)=f(x) and solving for t. It is mentioned that most functions are not periodic, but if the equation holds for all x, then the function is periodic with period t. However, there is confusion about how this equation can give the period of the function since it results in t being in terms of x. It is advised to use a string of symbols to represent t and ensure that t is not equal to zero to determine the period of the function. The speaker also reminds to conserve question marks as some people may not have access to many of them.
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?

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 $$\forall x,\ f(x)=f(x+\text{foo})$$ 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.

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.

## What is the period of a non-trigonometric function?

The period of a non-trigonometric function is the length of the interval over which the function repeats itself. This means that for any given input, the function will produce the same output after a certain interval.

## How do you find the period of a non-trigonometric function?

To find the period of a non-trigonometric function, you can set the function equal to itself with a positive integer added to the independent variable. Then, solve for the value of the independent variable. This will give you the period of the function.

## Can a non-trigonometric function have a negative period?

No, a non-trigonometric function cannot have a negative period. This is because the period is defined as a positive value representing the length of the interval over which the function repeats itself.

## What is the relationship between the period and frequency of a non-trigonometric function?

The period and frequency of a non-trigonometric function are inversely related. This means that as the period increases, the frequency decreases, and vice versa. The frequency is the number of repetitions of the function per unit time.

## Can a non-trigonometric function have an infinite period?

Yes, a non-trigonometric function can have an infinite period. This occurs when the function never repeats itself, meaning that there is no interval over which the function produces the same output. In this case, the function is said to have an aperiodic behavior.

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