## Functions of many variables, Mathematics

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There may be more than one independent variable which determines the value of y. The dimension of a function is determined by the number of independent variables in the domain of a function. For example:

y = f(x, z) is a two dimensional function.

y = f(x1, x2, ....xn) is an n-dimensional function.

### Example

In capital budgeting, the net present value (y) of an investment project is defined as a function of the net cash flows in different time periods, project's initial cash outlay, the firm's cost of capital, and the life of the project.

This relationship can be expressed functionally as:

y      = f(Ct, B, P, N)

where,

C­t    =     net cash flow in time period t (t = 1, 2, ....N)

B      =     the project's initial cash outlay

P      =     the firm's cost of capital

N      =     the life of the project

It is known that this function is:

 y  = f(Ct, B, P, N) = For any given values of the right hand side independent variables, we can determine the left hand side dependent variable in a unique manner.

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