- #1
Michael17
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Can anyone please help me with this.
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.
(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.
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.
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.
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.