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DumpmeAdrenaline

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Consider the case of a real function f for which f inverse exists.

1) We we are not used to having the y-axis (vertical axis) to denote the independent variable which it does in x=f-1(y). We rotate the system through positive 90 degree and reflect about the vertical to change the sense of the axis. One further adjustment to make is to relabel the horizontal axis x and the vertical axis y (the names we give to the axes are immaterial).

If we accept the convention that the independent variable must be always plotted along the horizontal axis in the left right sense and the independent variable be called x. Then the first figure on the top left is the appropriate graph of y=f(x) and the bottom figure would be the appropriate graph for y=f^-1(x). Which figures are appropriate for these relations x=f(y) and x=f^-1(y)?

I think x=f(y) denotes the relation for the top left figure and x=f^-1(y) for the bottom figure because names to the input and output are irrelevant.

1) We we are not used to having the y-axis (vertical axis) to denote the independent variable which it does in x=f-1(y). We rotate the system through positive 90 degree and reflect about the vertical to change the sense of the axis. One further adjustment to make is to relabel the horizontal axis x and the vertical axis y (the names we give to the axes are immaterial).

If we accept the convention that the independent variable must be always plotted along the horizontal axis in the left right sense and the independent variable be called x. Then the first figure on the top left is the appropriate graph of y=f(x) and the bottom figure would be the appropriate graph for y=f^-1(x). Which figures are appropriate for these relations x=f(y) and x=f^-1(y)?

I think x=f(y) denotes the relation for the top left figure and x=f^-1(y) for the bottom figure because names to the input and output are irrelevant.

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