 Scalar Multiple of a function: When we obtain a function c(x) by multiplying the given function f(x) by a constant k, the obtained function c(x) = kf(x) is called the scalar multiple of the function.
if f(x) = x^{2} + 1 then g(x)= 4f(x) = 4x^{2} + 4
 Sum of functions: A function s is called the sum of the functions f and g,
if s(x) = f(x) + g(x) and is denoted by f + g. Thus, (f + g)(x) = s(x)
 Difference of functions: A function d is called the difference of the functions f and g,
if d(x) = f(x)  g(x) and is denoted by f  g. Thus, (f  g)(x) = d(x)
 Product of functions: A function p is called the product of the functions f and g,
if p(x) = f(x)g(x) and is denoted by fg. Thus, (fg)(x) = p(x)
 Quotient of functions: A function q is called the quotient of the functions f by g,
if q(x) = f(x)/g(x), when g(x)≠0 for any x and is denoted by f/g. Thus, (f/g)(x) = q(x)
 Composite of functions: Let f be a function from X to Y and g be a function from Y to Z be two functions. We define a function h from X to Z by setting h(x) = g(f(x)).
To obtain h(x), we first take the fimage, f(X), of an element x of X. This f(x) ∈ Y, which is the domain of g. We then take the gimage of f(x), that is, g(f(x)), which is an element of Z.
