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6.6 Function Operations. Function Operation. Addition (f+g)(x) = f(x) + g(x) Multiplication (f * g)(x) = f(x) * g(x) Subtraction (f-g)(x) = f(x) – g(x) Division (f/g)(x) = f(x) / g(x) , g(x) ≠0. Example: Let f(x) = 5x 2 -4x and g(x) = 5x+1, find f+g and f-g. f+g = 5x 2 -4x + 5x+1
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Function Operation Addition (f+g)(x) = f(x) + g(x) Multiplication (f * g)(x) = f(x) * g(x) Subtraction (f-g)(x) = f(x) – g(x) Division (f/g)(x) = f(x) / g(x) , g(x)≠0
Example: Let f(x) = 5x2-4x and g(x) = 5x+1, find f+g and f-g. f+g = 5x2-4x + 5x+1 = 5x2+x+1 f-g = 5x2-4x –(5x+1) = 5x2-9x-1
Example 2: Let f(x) = 6x2+7x-5 and g(x) = 2x-1 Find f * g and f/g f*g = (6x2+7x-5) * (2x-1) = 12x3+8x2-17x+5 f/g = 6x2+7x-5 / (2x-1) = (3x+5)(2x-1) / (2x-1) = (3x+5) x≠1/2
Composition of Functions The composition of function g with function f is written as g ٥ f or (g ٥ f) (x) and is defined as : (g ٥ f) (x) = g ( f (x)) You evaluate the inner function first, then use your answer as the input of the outer function.
Example: Let f(x) = x-2 and g(x) = x2 evaluate (g ٥ f) (-5). (g ٥ f) (-5) = g (f (-5)) = g ( -5-2) = g(-7) = (-7)2 = 49 You Try: (f ٥ g) (-5) Answer: 23
What is (f ٥ g) (x) in general? f(g(x)) = f(x2) = x2 – 2 What about (g ٥ f) (x) = g ( f(x)) = g( x – 2 ) = (x-2)2 = x2 – 4x + 4 Typically f(g(x)) doesn’t equal g(f(x))
