SAT II Math II : Other Properties

Study concepts, example questions & explanations for SAT II Math II

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Example Questions

Example Question #51 : Properties Of Functions And Graphs

Define the functions  and  on the set of real numbers as follows:

Give the natural domain of the composite function .

Possible Answers:

Correct answer:


The natural domain of the composite function  is defined to be the intersection of the two sets.


One set is the natural domain of . Since  is defined to be the square root of an expression, the radicand must be nonnegative. Therefore,

This set is .


The other set is the set of numbers that the function  pairs with a number within the domain of . Since the radicand of the square root in  must be nonnegative, 

For  to fall within this set:

This set is .


, which is the natural domain.

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