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Composition of two functions - for which is in the domain...

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Composition of two functions: Basic Suppose that the functions and are defined as follows: . Find the following: . Given functions and , we can define a new function, , as follows: . This function is called the composition of with . Note that a value of this function is obtained by first evaluating the function at to obtain and then evaluating the function at to obtain . The domain of is the set of all values
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Unformatted text preview: for which is in the domain of . We can use this definition to find the values and for the functions and given in the problem. by definition of because by definition of because The answer is: Note: As we see in this problem, it is not necessarily the case that for given functions and and a given value of . For additional explanation, see your textbook: • Section 2.7: Combining Functions ....
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