### All SAT II Math II Resources

## Example Questions

### Example Question #1 : Other Properties

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.

Nadeem

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Zimindara College, Bachelor of Science, Applied Mathematics. University of Miami, Master of Science, Mathematics.

Farzad

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Oberlin College, Bachelor in Arts, Mathematics. Oberlin College, Bachelor of Science, Chemistry.