Algebra of real functions in math

List of Algebra of real functions

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

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

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

Multiplication of two real functions The product (or multiplication) of two real functions f:X→R and g:X→R is a function f_g:X→R defined by (f_g) (x) = f(x) g(x), for all x ∈ X

(f_g) (x) = f(x) g(x), for all x ∈ X

This is also called pointwise multiplication

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/g)(x)=f(x)/g(x) , provided g(x) ≠ 0, x ∈ X