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What is a function of fourier analysis?
It is to convert a function into a sum of sine (or cosine) functions so as to simplify its analysis.
Are the sum of two periodic functions always periodic?
yes
Is the infinite sum of continuous function continuous?
An infinite sum of continuous functions does not have to be continuous. For example, you should be able to construct a Fourier series that converges to a discontinuous function.
How can a new function be created by composing two existing functions?
You use the output of the first function as the input of the second function. For example, if your functions are sin() (the sine function) and root() (the square root function), you can combine them as:sin(root(x)) or: root(sin(x))
Is the graph of two continuous function is always continue?
Well, it sounds like a plausible statement, and maybe it would be true . But we haveno idea what the graph of two functions is.Perhaps you could graph the sum of two functions, or the difference of two functions,or their product, or their quotient. We believe that if the original two functions areboth continuous, then their sum and difference would also be continuous, but theirproduct and their quotient might not necessarily be continuous. However, we stilldon't know what the "graph of two functions" is.
