## Notation and meaning of functions

"m is the function of g" can be written as \(m = f(g)\). Meaning: m changes as the result of the variable g changing.

If g itself is a function of v, and their relation is written as \(g = F(v)\), the m can also be written as

$$m=f(F(v))$$

g is the value of \(F(v)\), and m is the value of \(f(g)\).

## Definition of function

One variable \(y\) is said to be the function of another variable \(x\) if for every possible value of \(x\) there is a corresponding value of \(y\). Written as

$$y = f(x)$$

\(x\) is the *independent* variable while \(y\) is the *dependent* variable.