Composition of Functions - Lecture Notes | MATH 150, Study notes of Mathematics

Download Composition of Functions - Lecture Notes | MATH 150 and more Study notes Mathematics in PDF only on Docsity! Section 2-7 1 Math 150 Lecture Notes Composition 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) Domain A ∩ B (f – g)(x) = f(x) – g(x) Domain A ∩ B (fg)(x) = f(x)g(x) Domain A ∩ B )( )( )( xg xf x g f =      Domain {x ∈ A ∩ B | g(x) ≠0} Given two function f and g, the composite function gf o (also called the composition of f and g) is defined by ))(())(( xgfxgf =o . The domain of gf o is the set of all x in the domain of g such that g(x) is in the domain of f. f x g gf o f(g(x)) g(x) Example 1: Find f + g, f – g, fg, and f/g and their domains. 4)( 2 −= xxf 2 2 )( + = x xg