Is (fg)(x) the same as (f(g(x))?

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The discussion clarifies that (fg)(x) represents the product of functions f and g, while f(g(x)) denotes the composition of these functions. The correct notation for function composition is h = f ∘ g. Additionally, the thread highlights a common misunderstanding regarding the relationship between function products and composition, particularly in the context of exponential functions.

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Can anyone please help me with this.

Is (fg)(x) the same as (f(g(x))?
 
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No, the first is the product of f and g while the second is the composition of f and g.
 
The notation that is frequently used for h which is the composition of f and g is:

h = f\circ g
 
Furthermore, the title of this thread indicates some misunderstanding, and has nothing to do with function products and pertains to function composition only when f is some kind of exponential function.

"f to the g" would be written as follows:
f^{g(x)}
 

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