A function from the set ℝ of real numbers (or a subset of ℝ) to ℝ. Thus, if f is a real function, then, for every real number x in the domain, a corresponding real number f(x) is defined. If a function f: S → ℝ is defined by giving a formula for f(x), without specifying the domain S, it is usual to assume that the domain is the largest meaningful subset S of ℝ. For example, if f(x) = 1/(x − 2), the domain would be taken to be ℝ\\ {2}; that is, the set of all real numbers not equal to 2. If $f(x)=\sqrt{9-x^2}$, the domain would be the closed interval [−3, 3].