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A function f from X to Y. The set of points in the red oval X is the domain of f. Graph of the real-valued square root function, f(x) = √ x, whose domain consists of all nonnegative real numbers. In mathematics, the domain of a function is the set of inputs accepted by the function.
Notation for the (principal) square root of x. For example, √ 25 = 5, since 25 = 5 ⋅ 5, or 5 2 (5 squared). In mathematics, a square root of a number x is a number y such that =; in other words, a number y whose square (the result of multiplying the number by itself, or ) is x. [1]
The function with domain does not have an inverse function. If we restrict x 2 {\displaystyle x^{2}} to the non-negative real numbers , then it does have an inverse function, known as the square root of x . {\displaystyle x.}
A square root of a number x is a number r which, when squared, becomes x: =. Every positive real number has two square roots, one positive and one negative. For example, the two square roots of 25 are 5 and −5. The positive square root is also known as the principal square root, and is denoted with a radical sign:
In mathematics, the radical symbol, radical sign, root symbol, or surd is a symbol for the square root or higher-order root of a number. The square root of a number x is written as , while the n th root of x is written as . It is also used for other meanings in more advanced mathematics, such as the radical of an ideal. In linguistics, the ...
This relation can be satisfied by any value of y equal to a square root of x (either positive or negative). By convention, √ x is used to denote the positive square root of x. In this instance, the positive square root function is taken as the principal branch of the multi-valued relation x 1/2.
Notations expressing that f is a functional square root of g are f = g [1/2] and f = g 1/2 [citation needed] [dubious – discuss], or rather f = g 1/2 (see Iterated function#Fractional_iterates_and_flows,_and_negative_iterates), although this leaves the usual ambiguity with taking the function to that power in the multiplicative sense, just as f ² = f ∘ f can be misinterpreted as x ↦ f(x)².
A subadditive function is a function:, having a domain A and an ordered codomain B that are both closed under addition, with the following property: ,, (+) + (). An example is the square root function, having the non-negative real numbers as domain and codomain: since ∀ x , y ≥ 0 {\displaystyle \forall x,y\geq 0} we have: x + y ≤ x + y ...