Presentation on theme: "Combinations of Functions"— Presentation transcript:
1Combinations of Functions Section 1.5CombinationsofFunctions
2Combinations of Functions Arithmetic Combinations of FunctionsThe domain of an arithmetic combination of functions f and g consistsof all real numbers that are common to the domains of f and g. In theCase of f(x)/g(x), there is the further restriction that g(x) 0.Sum, Difference, Product and Quotient Functions1. Sum2. Difference3. Product4. Quotient
5Combinations of Functions Definition of Composition of Two FunctionsThe composition of the function f with the function g isThe domain of f ◦ g is the set of all x in the domain of g suchthat g(x) is in the domain of f.
6Combinations of Functions How to from the composite of two functions:Given:Step 1: Think of f(x) as being the primary function and g(x) being thesecondary function. To form the composite substitute thesecondary function into the primary function.Definition of compositeSubstitution of 4 – x2 for x in x + 2Step 2: Simplify the result.
7Combinations of Functions How to from the composite of two functions (cont.):Given:Step 1: Think of g(x) as being the primary function and f(x) being thesecondary function. To form the composite substitute thesecondary function into the primary function.Definition of compositeSubstitution of x + 2 for x in 4 – x2Step 2: Simplify the result.
8Combinations of Functions How to find the numeric value for the combination of two functionsGiven:Step 1: Find g(2).Step 2: Take the value for g(2) andsubstitute it into f(x).Step 3: The answer found in step 2 is thenumeric value for
9Combinations of Functions How to find numeric values of composite graphically.Given:Step 1: Graph both functions on individual graphs.Step 2: Find g(0)g(0) = 1Step 3: Take the valuefrom Step 2 andsubstitute It in forx in f(x). Find itsvalue on the graph.f(1) = -2f(x) = x2 - 3g(x) = 2x + 1