Other Properties

Help Questions

SAT Math › Other Properties

Questions 1 - 1

1

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

$f (x) = \sqrt{x- 16}$

$g(x) = \sqrt{x- 4}$

Give the natural domain of the composite function $f \circ g$ .

$[260, \infty)$

$[4, \infty)$

$[16, \infty)$

$[32, \infty)$

$[0 , \infty)$

Explanation

The natural domain of the composite function $f \circ g$ 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,

$x - 4 \geq 0$

$x \geq 4$

This set is $[4, \infty)$ .

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,

$x - 16 \geq 0$

$x \geq 16$

For to fall within this set:

$g(x) \geq 16$

$\sqrt{x- 4} \geq 16$

$x - 4 \geq 256$

$x \geq 260$

This set is $[260, \infty)$ .

$[4, \infty) \cap [260, \infty) = [260, \infty)$ , which is the natural domain.

Return to subject

AI TutorYour personal study buddy

Question of the DayDaily practice to build your skills

FlashcardsStudy and memorize key concepts

WorksheetsBuild custom practice quizzes

AI SolverStep-by-step problem solutions

Learn by ConceptMaster concepts step by step

Diagnostic TestsAssess your knowledge level

Practice TestsTest your skills with exam questions

GamesLearn through free games