Input variable in a function

Main Question or Discussion Point

For a generic function $f$, why is that we use the variable $x$ as the argument of the function? What is the significance of this variable in regards to the object that is the function? Does it denote what the function is able to transform? i.e., $f(z)$ usually denotes a function that takes complex numbers as inputs, while $f(x)$ represents real numbers as inputs... In addition, would this be the case for functions in physics? i.e., $x(t)$ denotes the displacement function that only takes time as input? Besides this information, what is the significance of the having a variable as an input to a function?

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Homework Helper
For a generic function $f$, why is that we use the variable $x$ as the argument of the function? What is the significance of this variable in regards to the object that is the function? Does it denote what the function is able to transform? i.e., $f(z)$ usually denotes a function that takes complex numbers as inputs, while $f(x)$ represents real numbers as inputs... In addition, would this be the case for functions in physics? i.e., $x(t)$ denotes the displacement function that only takes time as input? Besides this information, what is the significance of the having a variable as an input to a function?