Operations on functions

  1. 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) = x2 + 1 then g(x)= 4f(x) = 4x2 + 4
  2. 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)
  3. 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)
  4. 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)
  5. 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)
  6. 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 f-image, f(X), of an element x of X. This f(x) ∈ Y, which is the domain of g. We then take the g-image of f(x), that is, g(f(x)), which is an element of Z.





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