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Composition of two function domain and range

# Composition of two function domain and range - Note that...

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Composition of two functions: Domain and range Two functions and are defined in the figure below. Find the domain and range of the composition . Write your answers in set notation. Given functions and , the composition of with , written , is defined as follows: . In other words, to obtain the value of the function at an input value , first evaluate the function at to obtain , and then evaluate the function at to obtain . Of course, the function has to be defined at the value , that is, must be in the domain of . Otherwise, is not defined. Thus, the domain of is equal to the set of all elements in the domain of for which is in the domain of . For the current problem, a sketch of the composition of with is shown in the figure below.

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Unformatted text preview: Note that the range of is not equal to the domain of . For instance, is an element of the domain of , but is not an element of the domain of . Thus, the value is not defined. We can do a similar analysis with the other elements of the domain of : is an element of the domain of is an element of the domain of is an element of the domain of is an element of the domain of is not an element of the domain of Therefore, the domain of is . To find the range of , we find the images of those values under , as follows: Therefore, the range of is . The function can be summarized as follows: Thus, the answer is: For additional explanation, see your textbook: Section 2.7: Combining Functions Domain of = Range of = ....
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Composition of two function domain and range - Note that...

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