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Helo, given ##f:R^n\rightarrow R^m## and ##g:R^m\rightarrow R^e## both class ##C^m##. Is the composition ##g\circ f## of class ##C^m## ?.
Composition of functions is an operation that combines two or more functions to create a new function. It is denoted by (f · g)(x) and is read as "f of g of x". This means that the output of g(x) is used as the input for f(x).
To evaluate a composition of functions, you first need to identify the inner and outer functions. Then, substitute the input value into the inner function and use the resulting output as the input for the outer function. Finally, simplify the expression to get the final value.
The composition of functions is an operation that combines two functions to create a new function. The product of functions, on the other hand, is an operation that multiplies two functions together to create a new function. In composition, the output of one function is used as the input for the other function, while in product, the functions are multiplied together using the same input value.
No, not all functions can be composed. In order for two functions to be composed, the output of the inner function must be in the domain of the outer function. This means that the input value for the inner function must also be a valid input for the outer function.
The associative property of composition of functions states that the order in which functions are composed does not matter. In other words, (f · g) · h = f · (g · h). This means that you can group functions in any way you want when composing them, and the result will be the same.