Function 

f(x)

Definition: a relationship between two variables x and y. If a numerical value is assigned to x, there is one and only one corresponding value for y.

• Note: there is nothing special about the variables x and y. We can use any variables we like.
• Often to represent how processes change in space and time.

Inverse Function

f^-1(x)

Definition: a reverse of the operation y(x) which maps x→y; the inverse maps y→x, returning x(y).

• Examples: e^x and ln(x), sin(x) and sin^-1(x), x and 1/x.
• Note: not all functions are invertible, and some function inverses are undefined for some values. Example: 1/x is not defined at x=0.

Definition: a quantity that, in the problem of interest, doesn't depend on any other variable.

Examples:

• In f(x), x is the independent variable.
• In x(t) = x₀ + vt + ½at², t is the dependent variable.

Definition: a quantity in the problem that depends on another variable.

Examples:

• In u = sin(x), u is the dependent variable.
• In x(t) = x₀ + vt + ½at², x is the dependent variable.