No, H = F-G holds only for x = a and x = b. There isn't any information for any x other than a or b.Simon Bridge said:Can you come up with a sample F and G so that H=F-G holds for x=a and x=b but does not hold in general?
The relationship between H(x), F(x), and G(x) is that they are all mathematical functions that describe the relationship between variables. H(x) is a function that represents the hypothesis or prediction based on the data, F(x) is a function that represents the observed data, and G(x) is a function that describes the underlying relationship between the variables.
H(x) and F(x) can be used to determine the validity of G(x) by comparing the predictions made by H(x) to the actual data represented by F(x). If H(x) accurately predicts the data, it can be concluded that G(x) is a valid representation of the relationship between the variables.
No, G(x) is not always a direct result of H(x) and F(x). While H(x) and F(x) can be used to determine the underlying relationship between variables, G(x) may also be influenced by other factors or variables that are not represented in the data or prediction.
No, H(x) and F(x) cannot be used interchangeably to describe the relationship between variables. H(x) represents a prediction based on the data, while F(x) represents the actual observed data. While they may both describe the relationship between variables, they serve different purposes and cannot be used interchangeably.
The generalization of the relationship between H(x), F(x), and G(x) can be applied in scientific research by using it as a framework for developing hypotheses and making predictions based on data. It can also be used to evaluate the accuracy and validity of these predictions and to further investigate the underlying relationship between variables.