Addition of two real functions Let f : X → R and g : X → R be any two real functions, where X ⊂ R . Then, we define ( f + g ): X → R by ( f + g ) ( x ) = f ( x ) + g ( x ), for all x ∈ X. Fig . f(x)= x x ,x ‘ 0and0for = RELATIONS AND FUNCTIONS Subtraction of a real function from another Let f : X → R and g : X → R be any two real functions, where X ⊂ R .
Then, we define ( f – g ) : X → R by ( f – g ) ( x ) = f ( x ) – g ( x ), for all x ∈ X. (iii) Multiplication by a scalar Let f : X → R be a real valued function and α be a scalar. Here by scalar, we mean a real number. Then the product α f is a function from X to R defined by ( α f ) ( x ) = α f ( x ), x ∈ X.
(iv) Multiplication of two real functions The product (or multiplication) of two real functions f :X → R and g :X → R is a function fg :X → R defined by ( fg ) ( x ) = f ( x ) g ( x ), for all x ∈ X. This is also called pointwise multiplication. (v) Quotient of two real functions Let f and g be two real functions defined from X → R , where X ⊂ R . The quotient of f by g denoted by f g is a function defined by , f f x g g x , provided g ( x ) ≠ , x ∈ X Example Let f ( x ) = x and g ( x ) = x + be two real functions.Find ( f + g ) ( x ), ( f