Algebraic Operations On Functions

Algebraic Operations On Functions

(a) If f and g are two functions and let their domains be D₁ & D₂, then sum of the function f + g is defined for all values of x ∈ D₁ ∩ D₂

(f + g)x = f(x) + g(x)

(b) If f and g are two functions, then the pointwise product of fg is defined for

all x ∈ D₁ ∩ D₂ by

(fg)x = f(x).g(x)

(c) If k is any real number and f is a function then kf is defined for all x ∈ D1 by

(kf)x = k f(x).

(d) If f and g are function then f/g is defined for all

x ε D₁ ∩ D₂ ∩ {x : g(x) ≠ 0}by (f/g)x = F(x)/g(x), g(x) ≠ 0.