How to find the period of this function

In summary, the conversation discusses the equation f(x)+f(x+4)=f(x+2)+f(x+6) and how to relate it to the function g(x)=f(x)+f(x+4) with a period of 2. The approach suggested is to set g(x)=f(x)+f(x+4) and then observe that the left-hand side is g(x) and the right-hand side is g(x+2), leading to the conclusion that g(x)=g(x+2). However, it is unclear how to relate this to f(x) and whether trial and error is necessary.
  • #1
abhip
9
0
f(x)+f(x+4)=f(x+2)+f(x+6) where all functions are real valued
 
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  • #2
Write g(x)=f(x)+f(x+4). Then it's easy to see that the left-hand side is g(x) and the right hand side is g(x+2), so g(x)=g(x+2). That seems to be where I would start.
 
  • #3
Thank you very much for the approach it was helpful but after setting g(x)=f(x)+f(x+4) and knowing the fact g(x) has a period 2 how to relate if to f(x).Is there any approach to do so or do i have to opt for trial and error.
 
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1. What is the period of a function?

The period of a function is the length of the interval over which the function repeats itself. In other words, it is the distance between two consecutive peaks or troughs on a graph of the function.

2. How do I find the period of a function?

To find the period of a function, you need to identify the value of the variable that causes the function to repeat itself. This is usually found in the argument of a trigonometric function or within a set of parentheses in an algebraic function. Once you have identified this value, you can use it to calculate the period using the appropriate formula.

3. What is the difference between the period and the frequency of a function?

The period and frequency of a function are inversely related. The period is the length of time it takes for a function to complete one full cycle, while the frequency is the number of cycles that occur in one unit of time. In other words, the period is the reciprocal of the frequency.

4. Can a function have a negative period?

No, a function cannot have a negative period. The period is always a positive value, as it represents the distance between two consecutive repetitions of the function. However, a function can have a negative frequency, which indicates a reversal of the direction of the function's graph.

5. How does the period of a function affect its graph?

The period of a function determines the frequency of its wave-like pattern. A shorter period results in a higher frequency, causing the graph to appear more compressed or "squished" horizontally. Conversely, a longer period leads to a lower frequency and a wider, more spread out graph.

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