What is the significance of using a variable as an input to a function?

[Mr Davis 97]

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?

 

[symbolipoint]

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?

Cultural practice, and a guess that the ordered letters at the far right of the list contain some elements which are less common in words that use those letters, so only a guess, they seemed convenient choices to represent uknown numbers. This makes one think of how scientists who first discovered some radiation and did not know what to call it, so decided on X-Rays. "We do not know what kind of rays these are and so we will call these mystery rays, X Rays".

We are not restricted just to x as the function argument. We can use any letter we want. Certain ones are common for different purposes.