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

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Homework Help Overview

The discussion revolves around the notation and interpretation of functions, specifically whether (fg)(x) is equivalent to (f(g(x))). The subject area pertains to function operations, including multiplication and composition.

Discussion Character

  • Conceptual clarification

Approaches and Questions Raised

  • Participants explore the distinction between function multiplication and composition, with some providing alternative notations for clarity.

Discussion Status

There is an active exploration of the differences between the two notations, with participants offering clarifications and alternative representations. The discussion indicates a misunderstanding that is being addressed, but no consensus has been reached.

Contextual Notes

Some participants suggest that the misunderstanding may relate specifically to cases involving exponential functions, indicating a potential area of confusion regarding notation.

Michael17
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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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