- #1
coverband
- 171
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where f and g are finctions of x
please thanks
please thanks
ObsessiveMathsFreak said:This appears to be the definition of the sum of two functions. It is valid as long as f and g have the same domains and ranges.
The notation (f+g)(x) represents the composition of two functions, f(x) and g(x). It means that the output of g(x) is used as the input for f(x), or in other words, g(x) is "plugged in" to f(x).
To prove that two functions are equal, you must show that they have the same domain and range, and that they produce the same output for every input. In the case of (f+g)(x) = f(x) + g(x), you would need to show that for any given value of x, both sides of the equation produce the same result.
It depends on the specific functions f(x) and g(x). Some combinations of functions can be simplified, while others cannot. For example, if f(x) = 2x and g(x) = x^2, then (f+g)(x) = 2x + x^2, which cannot be simplified further. Other combinations, such as f(x) = 2x and g(x) = -2x, can be simplified to (f+g)(x) = 0.
Yes, (f+g)(x) is commutative, meaning that the order in which the functions are composed does not affect the result. This can be seen in the equation (f+g)(x) = f(x) + g(x), where the order of f(x) and g(x) can be switched without changing the outcome.
As mentioned in the answer to the first question, (f+g)(x) is a composition of two functions, f(x) and g(x). However, (f+g)(x) is different from the traditional notation for function composition, which is written as f(g(x)). In this case, (f+g)(x) is a combination of two functions, while f(g(x)) is a function that takes the output of g(x) as the input for f(x).