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# Composition of two function advanced - is the interval Now...

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Composition of two functions: Advanced For the real valued functions and , find the composition and specify its domain using interval notation . Domain of : The composition of functions and is defined by for all such that is in the domain of and is in the domain of . For the current problem, and , and we have . The function machine diagram shown in Figure 1 summarizes this composition. To find the domain of , we first find the domain of and the domain of . The real valued function is defined precisely when , that is, when . Therefore, the domain of is Figure 1

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the interval . The function is defined for all real numbers. That is, the domain of
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Unformatted text preview: is the interval . Now we are ready to find the domain of , which consists of all that satisfy both of the following conditions: Condition 1: is in the domain of , Condition 2: is in the domain of . Because the domain of is , condition 1 is satisfied by all such that . Because the domain of is , the values are always in the domain of . That is, condition 2 is always satisfied. So conditions 1 and 2 are satisfied by all such that . Therefore, using interval notation , the domain of is . The answer is: For additional explanation, see your textbook: • Section 2.7: Combining Functions and Domain of : ....
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Composition of two function advanced - is the interval Now...

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