In this video I go over the definitions and notations involved in combining two different functions. What I mean by combining functions, I mean adding, subtracting, multiplying and dividing two functions.

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Combination of Functions

Algebra of Functions

Let f and g be functions with domains A and B.

Then the functions f + g, f – g, fg, and f/g are defined as follows:

• (f + g)(x) = f(x) + g(x) with domain = A ∩ B
• (f – g)(x) = f(x) – g(x) with domain = A ∩ B
• (fg)(x) = f(x)g(x) with domain = A ∩ B
• (f/g)(x) = f(x)/g(x) with domain = {x ϵ A ∩ B|g(x) ≠ 0}
  • ϵ = element of or inside.
  • | = except
  • f/0 is not defined.

Example

Solution