Answer:
[tex]x \le 3[/tex]
[tex]x \ge 0[/tex]
Step-by-step explanation:
The functions, missing from the question are:
[tex]f(x) = \sqrt{3 - x[/tex]
[tex]f(x) = \sqrt{3 x[/tex]
Required
Determine the domain
To get the domain, means we want to get the possible values of x.
(a)
[tex]f(x) = \sqrt{3 - x[/tex]
Equate 3 - x to 0
[tex]3 - x = 0[/tex]
Solve for x
[tex]-x = -3[/tex]
[tex]x = 3[/tex]
From the calculated value of x above;
When x exceeds 3; f(x) = undefined
So: the domain is:
[tex]x \le 3[/tex]
(b)
[tex]f(x) = \sqrt{3x[/tex]
Equate 3x to 0
[tex]3x = 0[/tex]
Solve for x
[tex]x = 0[/tex]
From the calculated value of x above;
When x falls below 0; f(x) = undefined
So: the domain is:
[tex]x \ge 0[/tex]
