SAT II Math II : Other Properties

Example Questions

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 .

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.