Function f Function
... two different elements in the domain have the same element in the range. The definition of a one-to-one function can be written algebraically as follows: A function f(x) is one-to-one if x1 is not equal to x2 (x1 and x2 any elements of the domain) then f(x1) is not equal to f(x2). In other words, fo ...
... two different elements in the domain have the same element in the range. The definition of a one-to-one function can be written algebraically as follows: A function f(x) is one-to-one if x1 is not equal to x2 (x1 and x2 any elements of the domain) then f(x1) is not equal to f(x2). In other words, fo ...
Ch2-Sec2.1
... Vertical Line Test for a Function If you have the graph of an equation, there is an easy way to determine if it is the graph of an function. It is called the vertical line test which states that: An equation specifies a function if each vertical line in the coordinate system passes through at most ...
... Vertical Line Test for a Function If you have the graph of an equation, there is an easy way to determine if it is the graph of an function. It is called the vertical line test which states that: An equation specifies a function if each vertical line in the coordinate system passes through at most ...
Function of several real variables
In mathematical analysis, and applications in geometry, applied mathematics, engineering, natural sciences, and economics, a function of several real variables or real multivariate function is a function with more than one argument, with all arguments being real variables. This concept extends the idea of a function of a real variable to several variables. The ""input"" variables take real values, while the ""output"", also called the ""value of the function"", may be real or complex. However, the study of the complex valued functions may be easily reduced to the study of the real valued functions, by considering the real and imaginary parts of the complex function; therefore, unless explicitly specified, only real valued functions will be considered in this article.The domain of a function of several variables is the subset of ℝn for which the function is defined. As usual, the domain of a function of several real variables is supposed to contain an open subset of ℝn.