Function x is called independent variable, y is called dependent variable, so what is f exactly?

Function x is called independent variable, y is called dependent variable, so what is f exactly?

F is called the law of correspondence
For example: y = f (x) = x & # 178;, the corresponding rule from the independent variable x to the dependent variable y is to square the independent variable

Given that y is the inverse proportional function of X, when x = - 5, y = 2, find the analytic expression and the value range of the independent variable

Y is the inverse proportional function of X
y=k/x
When x = - 5, y = 2
2=k/(-5)
k=-10
The analytic formula y = - 10 / X
The value range of independent variable
x≠0
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The solution of the system of equations x + y = 8mx − 2Y = 2m satisfies 2x-5y = - 1, and the value of M is obtained

To solve the equations x + y = 8mx − 2Y = 2m, we get x = 6my = 2m, substitute x = 6m, y = 2m into 2x-5y = - 1, we get 2 × 6m-5 × 2m = - 1, we get m = - 12