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The image of a function f(x 1, x 2, …, x n) is the set of all values of f when the n-tuple (x 1, x 2, …, x n) runs in the whole domain of f.For a continuous (see below for a definition) real-valued function which has a connected domain, the image is either an interval or a single value.
For example, let f(x) = 6x 4 − 2x 3 + 5, and suppose we wish to simplify this function, using O notation, to describe its growth rate as x approaches infinity. This function is the sum of three terms: 6x 4, −2x 3, and 5. Of these three terms, the one with the highest growth rate is the one with the largest exponent as a function of x ...
Dana Scott's LCF language [1] was a stage in the evolution of lambda calculus into modern functional languages. This language introduced the let expression, which has appeared in most functional languages since that time. The languages Scheme, [2] ML, and more recently Haskell [3] have inherited let expressions from LCF.
In numerical analysis, multivariate interpolation or multidimensional interpolation is interpolation on multivariate functions, having more than one variable or defined over a multi-dimensional domain. [1] A common special case is bivariate interpolation or two-dimensional interpolation, based on two variables or two dimensions.
A variant of the 3-satisfiability problem is the one-in-three 3-SAT (also known variously as 1-in-3-SAT and exactly-1 3-SAT). Given a conjunctive normal form with three literals per clause, the problem is to determine whether there exists a truth assignment to the variables so that each clause has exactly one TRUE literal (and thus exactly two ...
Multivalued functions of a complex variable have branch points. For example, for the nth root and logarithm functions, 0 is a branch point; for the arctangent function, the imaginary units i and −i are branch points. Using the branch points, these functions may be redefined to be single-valued functions, by restricting the range.
The computation of f(π ⁄ 6) = 1 ⁄ 2 = g 5 (π ⁄ 6) is shown. The notion f 1/n must be used with care when the equation g n (x) = f(x) has multiple solutions, which is normally the case, as in Babbage's equation of the functional roots of the identity map.
That is, the partial derivative of z with respect to x at (1, 1) is 3, as shown in the graph. The function f can be reinterpreted as a family of functions of one variable indexed by the other variables: (,) = = + +. In other words, every value of y defines a function, denoted f y, which is a function of one variable x. [6] That is, = + +.