Function Differences: f and f(n) vs. (f \circ g)(n)

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The discussion clarifies the distinction between a function f and its value f(n) at a specific point n. The composition operator (f \circ g)(n) cannot be expressed as f(n) \circ g(n) because the operator acts on functions rather than their output values. Instead, the correct formulation is f(g(n)), which applies function g to n first and then applies function f to the result. This highlights the importance of understanding function notation and composition in mathematics. The conversation emphasizes the correct application of function operations to avoid confusion.
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What is exactly the difference between f and f(n) and why can't we write (f \circ g)(n) as f(n) \circ g(n)?
 
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f is the function, f(n) is the value of the function at the point n. The ball operator \circ acts on functions, not values, so your second expression is wrong.
 
You can, however, write it as f(g(n)).
 
u can write it
no proplem...i thenk
 
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