Multiplication of Two Real Functions
Let f : X → R and g : X → R be any two real functions, where X ⊆ R. Then product of these two functions i.e. f ∗ g : X → R is defined by
(f × g) (x) = f (x) g (x) ∀ x ∈ X
Let D(f) and D(g) be the domain of function “f” and “g” respectively. In this case also the domain
D(f × g) = D(f) ∩ D(g)
Example: Given f(x) = x2 + 1 and g(x) = 1/x. Find (f × g)(x).
Solution:
(f × g)(x) = f(x) g(x) = (x2 + 1)(1/x) = [Tex]\frac{x^{2} + 1}{x}[/Tex]. Domain remains the same as previous example in this case too.
Algebra of Real Functions
The algebra of real functions refers to the study and application of algebraic operations on functions that map real numbers to real numbers.
A function can be thought of as a rule or set of rules which map an input to an output knows as its image. It is represented as x ⇢ Function ⇢ y. A real function refers to a function that maps real numbers to real numbers.
Algebra of real functions involves algebraic operations between two or more real functions. In this article we will learn in detail about algebra of real functions such addition, subtraction, multiplication and division between real function.