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QUBStudent
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hi, max{f(x),g(x)}=1/2[(f + g) + |f - g|] is the equation of the maximum of two functions on the real axis. Can anyone give me a hint on how to show where this equation comes from or how it is derived
The notation "max{f(x),g(x)}" means to take the larger value between f(x) and g(x). It is used to find the maximum value between two functions.
To prove this equation, we can use the definition of max function: max{a,b} = 1/2(a+b+|a-b|). By substituting f(x) and g(x) for a and b, we get max{f(x),g(x)} = 1/2(f(x)+g(x)+|f(x)-g(x)|). Since max{f(x),g(x)} is equal to the larger value between f(x) and g(x), we can rearrange the equation to get max{f(x),g(x)} = 1/2[(f+g) + |f-g|].
The absolute value ensures that we always get a positive value for the difference between f(x) and g(x). This is important because we want to find the larger value between the two functions, regardless of whether it is f(x) or g(x).
Yes, this equation can be applied to functions with multiple variables as long as the functions are continuous and differentiable. The max function can be extended to multiple variables by taking the maximum value of each variable.
This equation is useful in real-world applications where we need to compare two functions and determine the maximum value between them. For example, in optimization problems, we may need to find the maximum value of a function to determine the best solution. This equation can also be used in statistics to compare two sets of data and find the larger value between them.