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The sum f + g f g x f x g x This just says that to find the sum of two functions, add them together. You should simplify by finding like terms. f x 2 x 3 g x 4 x 1 2 3 f g 2x 3 4x 1 2 3 4x 2x 4 3 2 Combine like terms & put in descending order The difference f - g f g x f x g x To find the difference between two functions, subtract the first from the second. CAUTION: Make sure you distribute the – to each term of the second function. You should simplify by combining like terms. f x 2 x 3 2 g x 4 x 1 3 f g 2x 3 4x 1 2 3 Distribute negative 2 x 3 4 x 1 4 x 2 x 2 2 3 3 2 The product f • g f g x f x g x To find the product of two functions, put parenthesis around them and multiply each term from the first function to each term of the second function. f x 2 x 3 g x 4 x 1 2 3 f g 2x 3 4x 1 2 3 8 x 2 x 12 x 3 5 2 3 FOIL Good idea to put in descending order but not required. The quotient f /g f f x x g x g To find the quotient of two functions, put the first one over the second. f x 2 x 3 2 f 2x 3 3 g 4x 1 2 g x 4 x 1 3 Nothing more you could do here. (If you can reduce these you should). So the first 4 operations on functions are pretty straight forward. The rules for the domain of functions would apply to these combinations of functions as well. The domain of the sum, difference or product would be the numbers x in the domains of both f and g. For the quotient, you would also need to exclude any numbers x that would make the resulting denominator 0. Acknowledgement I wish to thank Shawna Haider from Salt Lake Community College, Utah USA for her hard work in creating this PowerPoint. www.slcc.edu Shawna has kindly given permission for this resource to be downloaded from www.mathxtc.com and for it to be modified to suit the Western Australian Mathematics Curriculum. Stephen Corcoran Head of Mathematics St Stephen’s School – Carramar www.ststephens.wa.edu.au