![]() ![]() Functions involving more than two variables (called multivariable or multivariate functions) also are common in mathematics, as can be seen in the formula for the area of a triangle, A = b h/2, which defines A as a function of both b (base) and h (height). For example, the formula for the area of a circle, A = π r 2, gives the dependent variable A (the area) as a function of the independent variable r (the radius). Many widely used mathematical formulas are expressions of known functions. In addition to f( x), other abbreviated symbols such as g( x) and P( x) are often used to represent functions of the independent variable x, especially when the nature of the function is unknown or unspecified. The set of values of x is called the domain of the function, and the set of values of f( x) generated by the values in the domain is called the range of the function. To use the language of set theory, a function relates an element x to an element f( x) in another set. That is, f( x) can not have more than one value for the same x. This relationship is commonly symbolized as y = f( x)-which is said “ f of x”-and y and x are related such that for every x, there is a unique value of y. If a variable y is so related to a variable x that whenever a numerical value is assigned to x, there is a rule according to which a unique value of y is determined, then y is said to be a function of the independent variable x. The modern definition of function was first given in 1837 by the German mathematician Peter Dirichlet: ![]() Functions are ubiquitous in mathematics and are essential for formulating physical relationships in the sciences. SpaceNext50 Britannica presents SpaceNext50, From the race to the Moon to space stewardship, we explore a wide range of subjects that feed our curiosity about space!įunction, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).Learn about the major environmental problems facing our planet and what can be done about them! Saving Earth Britannica Presents Earth’s To-Do List for the 21st Century.Britannica Beyond We’ve created a new place where questions are at the center of learning.100 Women Britannica celebrates the centennial of the Nineteenth Amendment, highlighting suffragists and history-making politicians.COVID-19 Portal While this global health crisis continues to evolve, it can be useful to look to past pandemics to better understand how to respond today.Student Portal Britannica is the ultimate student resource for key school subjects like history, government, literature, and more.Demystified Videos In Demystified, Britannica has all the answers to your burning questions.This Time in History In these videos, find out what happened this month (or any month!) in history.#WTFact Videos In #WTFact Britannica shares some of the most bizarre facts we can find.Britannica Classics Check out these retro videos from Encyclopedia Britannica’s archives.Britannica Explains In these videos, Britannica explains a variety of topics and answers frequently asked questions.
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