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ecastro

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Thank you in advance.

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In summary, the conversation revolves around the function f(x,y) being represented as f(y) later in the discussion. It is unclear if this change in representation implies anything, but the writer may have been being sloppy. It is possible that the function f(y) has its x value fixed, but it's impossible to be sure without knowing the full context.

- #1

ecastro

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- 8

Thank you in advance.

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- #2

blue_leaf77

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- #3

ecastro

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- #4

Ssnow

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1)is fixed before ...

2)doesn't appear in the equation as variable ...

3) there is an implicit dependence ##f(y(x))## so ##f## is a functional ...

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ecastro

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##f \left(x, y\right) = A \left(\frac{x}{x_0}\right) \left(\frac{y_0}{y}\right)^{\frac{1}{2}}##

So, it appears as a variable in the equation, and it doesn't seem to be a functional. The variables ##A##, ##x_0## and ##y_0## are constants.

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Ssnow

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- #7

Mark44

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ecastro said:

Thank you in advance.

This seems to me like the writer was being sloppy. The notation f(x, y) indicates a function of two variables. If x is held fixed at ##x_0##, then you have ##f(x_0, y)##, which is effectively a function of y alone. Clearer would be to say that ##f(x_0, y) = g(y)##, so as to not reuse f now appearing as a function of a single variable.ecastro said:

- #8

ecastro

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Mark44 said:This seems to me like the writer was being sloppy.

I think so too... Anyway, does everyone agree that the function ##f\left( y\right)## is a function with ##x = x_0##?

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Samy_A

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It's impossible to be sure without knowing the full context.ecastro said:I think so too... Anyway, does everyone agree that the function ##f\left( y\right)## is a function with ##x = x_0##?

It is a reasonable hypothesis, but x could also be some other fixed number in the calculation where the author uses f(y) instead of f(x,y).

- #10

ecastro

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Sorry, let me re-phrase:

Is the function ##f\left( y\right)## has its ##x## value fixed?

Is the function ##f\left( y\right)## has its ##x## value fixed?

- #11

Samy_A

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##f(y)## has no dependence on ##x##, so if this ##f## refers to the same ##f## used in the definition of ##f(x,y)##, then yes, it most probably means that ##x## is considered fixed in the calculation. If not, it is very sloppy indeed.ecastro said:Sorry, let me re-phrase:

Is the function ##f\left( y\right)## has its ##x## value fixed?

- #12

ecastro

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Thank you very much! Your help is highly appreciated.

A function is a mathematical concept that relates an input value to an output value. It is often represented as f(x) and can be thought of as a machine that takes an input and produces an output.

To represent a function means to express it in a specific form or format that shows the relationship between the input and output values. This can be done through mathematical equations, graphs, tables, or other visual representations.

A change in representing a function can alter its meaning by changing the way the input and output values are related. For example, converting a function from an equation to a graph may make it easier to visualize and understand, but the underlying mathematical relationship remains the same.

Yes, a function can have multiple representations. As long as the underlying mathematical relationship between the input and output values remains the same, it can be represented in different ways. Different representations may be useful for different purposes or to better understand the function.

Some common ways to represent a function include using mathematical equations, graphs, tables, and verbal descriptions. Other methods may include using computer programs, diagrams, or real-world examples to represent the function.

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