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What is function and relation?
All functions are relations with the condition that each element of the domain is paired with only one element of the range. A relation is any pairing of numbers from the domain to the range.
Would the domain be something other than all real numbers provide an example?
It could be a subset: for example, for the function y = log(x), the domain is x > 0. There are many functions whose domain is the complex plane.
Are bounded domain functions periodic?
No. You can always "cheat" to prove this by simply giving the function's domain a bound.Ex: f: [0,1] --> RI simply defined the function to have a bounded domain from 0 to 1 mapping to the codomain of the set of real numbers. The function itself can be almost anything, periodic or not.Another way to "cheat" is to simply recognize that all functions having a domain of R are bounded functions, by definition, in the complex plane, C.(Technically, you would say a non-compact Hermitian symmetric space has a bounded domain in a complex vector space.) Obviously, those functions include non-periodic functions as well.
True or false. When you compose two functions. The domain and the range of the original functions does influence the domain and the range of their composition?
true
When you compose two functions the domain and range of the original functions does influence the domain and range of their composition. True or False?
True.
