except and its range is also all real numbers except . The graph of f is given in Fig . . Fig .
(v) The Modulus function The function f : R → R defined by f ( x ) = | x | for each x ∈ R is called modulus function . For each non-negative value of x , f ( x ) is equal to x . But for negative values of x , the value of f ( x ) is the negative of the value of x, i.e., x,x f x x,x ≥ = − < The graph of the modulus function is given in Fig . .
(vi) Signum function The function f : R → R defined by if if if , f x , , > − < Fig . MATHEMATICS is called the signum function . The domain of the signum function is R and the range is the set {– , , }. The graph of the signum function is given by the Fig .
. Fig . (vii) Greatest integer function The function f : R → R defined by f ( x ) = [ x ], x ∈ R assumes the value of the greatest integer, less than or equal to x . Such a function is called the greatest integer function.
From the definition of [ x ], we can see that [ x ] = – for – ≤ x < [ x ] = for ≤ x < [ x ] = for ≤ x < [ x ] = for ≤ x < and so on. The graph of the function is shown in Fig . . .
. Algebra of real functions In this Section, we shall learn how to add two real functions, subtract a real function from another, multiply a real function by a scalar (here by a scalar we mean a real number), multiply two real functions and divide one real function by another.