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

  • Thread starter Michael17
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In summary, (fg)(x) and (f(g(x)) are different ways of representing the composition of two functions, with the order of operations being the main difference. However, they will always have the same value for any given input x due to the associative property of function composition. While they are equivalent in representing the same function, they may have different forms or expressions. An example of this is when f(x) = x^2 and g(x) = 2x, where (fg)(x) and (f(g(x)) have different forms, but will always have equal values.
  • #1
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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  • #2
No, the first is the product of f and g while the second is the composition of f and g.
 
  • #3
The notation that is frequently used for h which is the composition of f and g is:

[tex]h = f\circ g[/tex]
 
  • #4
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:
[tex]f^{g(x)}[/tex]
 

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

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

Yes, (fg)(x) and (f(g(x)) are both different ways of representing the composition of two functions, f and g.

Can you explain the difference between (fg)(x) and (f(g(x))?

(fg)(x) represents the function that results from first applying g to x and then applying f to the result. On the other hand, (f(g(x)) represents the function that results from first applying f to g(x) and then applying the result to x. In other words, the order of operations is different.

Do (fg)(x) and (f(g(x)) always have the same value?

Yes, the values of these two functions will always be equal for any given input x. This is because the composition of functions is an associative operation, meaning that the order in which the functions are composed does not affect the final result.

Are (fg)(x) and (f(g(x)) always equivalent?

Yes, (fg)(x) and (f(g(x)) are equivalent in that they represent the same function. However, they may be written differently or have different forms, such as using trigonometric identities or simplifying algebraically.

Can you give an example of (fg)(x) and (f(g(x)) being different?

One example is when f(x) = x^2 and g(x) = 2x. In this case, (fg)(x) = 2x^2 and (f(g(x)) = 4x^2. While the values of these two functions will always be equal, their forms are different.

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