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pawball
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have not seen this anywhere I've looked, anyone know?
The "◦" symbol in (f◦g)(x) represents the composition of two functions. It is read as "f composed with g" and indicates that the output of g is used as the input for f.
While both (f◦g)(x) and f(g(x)) represent the composition of two functions, their order of operations is different. (f◦g)(x) indicates that g is evaluated first and then the output is used as the input for f. In f(g(x)), g is evaluated first and then the output is used directly as the input for f.
Yes, (f◦g)(x) can be rewritten as f(g(x)). However, in some cases, it may be more useful to keep the composition form for easier understanding and visualization of the functions involved.
To evaluate (f◦g)(x), first evaluate g(x) and then use the output as the input for f. This can be done by substituting g(x) into the expression for f(x) and simplifying the resulting expression.
One limitation of using the composition notation is that the domains of f and g must be compatible. This means that the output of g must be a valid input for f. Additionally, the order of operations matters when evaluating (f◦g)(x), so it is important to pay attention to the order in which the functions are composed.