SAT II Math II : Properties of Functions and Graphs

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

varsity tutors app store varsity tutors android store

Example Questions

1 2 3 4 6 Next →

Example Question #51 : 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:

Explanation:

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.

1 2 3 4 6 Next →
Learning Tools by Varsity Tutors