Algebra 2 Name___________________________________ Operations on Functions Operations on Functions Operation Addition Subtraction Multiplication Division Definition Example Let f(x)=2x and g(x)=-x+5 (f+g)(x)=f(x)+g(x) (f-g)(x)=f(x)-g(x) (f g )(x)= f (x) g (x) 2x+(-x+5)=x+5 2x-(-x+5)=3x - 5 2x(-x+5)=-2x2+10x f f ( x) ( x) , g ( x) 0 g ( x) g 2x ,x 5 x5 Example 1: Given f(x) =x2 - 4 and g(x) =2x+1, find each function. Indicate any restrictions in the domain or range. a. (f+g)(x) b. (f-g)(x) You Try: Given f(x)=x2+5x-2 and g(x)=3x-2, find each function. a. (f+g)(x) b. (f-g)(x) Given f(x) =3x2+7x and g(x) =2x2-x-1, find each function. Indicate any restrictions in the domain. a. (f+g)(x) b. (f-g)(x) In Example 1, the functions f(x) and g(x) have the same domain of all real numbers. The functions (f+g)(x) and (f-g)(x) also have domains that include all real numbers. Under division, the domain of the new function is restricted by excluded values that cause the denominator to equal zero. Example 2: Given f(x) =x2+7x+12 and g(x) =3x-4, find each function. Indicate any restrictions in the domain or range. a. ( f g )( x) f b. (x) g You Try: Given f(x) =x2-7x+2 and g(x) = x+4, find each function. a. ( f g )( x) f (x) b. g Given f(x) = 3x2 - 2x+1 and g(x) =x-4, find each function. Indicate any restrictions in the domain and range. a. ( f g )( x) f (x) b. g Composition of Functions: Another method used to combine functions is a composition of functions. In a composition of functions, the results of one function are used to evaluate a second function. Suppose f and g are functions such that the range of g is a subset of the domain of f. Then the composition of function f g can be described by f g ( x) f g ( x) The composition of two functions may not exist. Given two functions f and g, f g (x) is defined only if the range of g(x) is a subset of the domain of f. Likewise, g f (x) is defined only if the range of f(x) is a subset of the domain of g. Example 3: Find f g (x) a) f(x) =2a-5, g(x)=4a You Try: Find f g (x) a) f(x)=x2+2 and g(x)=x-6 Example 4: Find g f (x) a) f(x) =2a-5, g(x)=4a You Try: Find g f (x) b) f(x)=x2+2 and g(x)=x-6 Example 5: Find f g (3) a) f(x) =2a-5, g(x)=4a You Try: Find f ( g (1)) b) f(x)=x2+2 and g(x)=x-6

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