# L11 - Lecture 11 Section 1.8 Combinations of Functions...

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Lecture 11: Section 1.8 Combinations of Functions Algebra of Functions Let u1D453 and u1D454 be two functions with domains u1D434 and u1D435 . We define some new functions: Name Definition Domain u1D453 ± u1D454 u1D453u1D454 u1D453 u1D454 ex. Given u1D453 ( u1D465 ) = u1D465 3 and u1D454 ( u1D465 ) = u1D465 . Find the function u1D453 u1D454 and its domain.

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ex. If u1D453 ( u1D465 ) = u1D465 and u1D454 ( u1D465 ) = 1 u1D465 , find the function u1D453 + u1D454 and its domian. ex. If u1D453 ( u1D465 ) = 1 u1D465 + 1 and u1D454 ( u1D465 ) = u1D465 u1D465 + 1 , find each function and its domain. 1) u1D453u1D454 2) u1D453 u1D454
Composition of Functions Def. Given two functions u1D453 and u1D454 , the composi- tion of function u1D453 with function u1D454 is defined by ( u1D453 u1D454 )( u1D465 ) = The domain of ( u1D453 u1D454 ) is the set of u1D465 in the domain of u1D454 such that u1D454 ( u1D465 ) is in the domain of u1D453 . g f ex. Let u1D453 = u1D465 2 and u1D454 = u1D465 3. Find the functions u1D453 u1D454 and u1D454 u1D453 .

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ex. If u1D453 ( u1D465 ) = 1 u1D465 + 2 and u1D454 ( u1D465 ) = 4 u1D465 1 , find the following functions and their domains.
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