Question

What is the domain for each function below? Choose the correct inequality symbol from the drop down menu and fill in the blank with the correct integer so that the appropriate domain for each is described. domain: x domain: x

Answer 1

Answer:

$x \le 3$

$x \ge 0$

Step-by-step explanation:

The functions, missing from the question are:

$f(x) = \sqrt{3 - x$

$f(x) = \sqrt{3 x$

Required

Determine the domain

To get the domain, means we want to get the possible values of x.

(a)

$f(x) = \sqrt{3 - x$

Equate 3 - x to 0

$3 - x = 0$

Solve for x

$-x = -3$

$x = 3$

From the calculated value of x above;

When x exceeds 3; f(x) = undefined

So: the domain is:

$x \le 3$

(b)

$f(x) = \sqrt{3x$

Equate 3x to 0

$3x = 0$

Solve for x

$x = 0$

From the calculated value of x above;

When x falls below 0; f(x) = undefined

So: the domain is:

$x \ge 0$