What is the domain of the function y = 2 StartRoot x minus 6 EndRoot?



choices:

Negative infinity less-than x less-than infinity

0 less-than-or-equal-to x less-than infinity

3 less-than-or-equal-to x less-than infinity

6 less-than-or-equal-to x less-than infinity

Respuesta :

Correct answer is D) 6 less-than-or-equal-to x less-than infinity

Step-by-step explanation:

Here we have  [tex]f(x) = 2(\sqrt{x-6})[/tex] . We need to find domain of this function . Let's find out:

⇒ [tex]f(x) = 2(\sqrt{x-6})[/tex]

Since, Inside term of a square root is always greater then or equal to zero i.e.

⇒ [tex]x-6\geq 0[/tex]

Adding 6 both sides we get:

⇒ [tex]x-6\geq 0[/tex]

⇒ [tex]x-6+6\geq 0+6[/tex]

⇒ [tex]x\geq 6[/tex]

Therefore , Domain of function [tex]f(x) = 2(\sqrt{x-6})[/tex] is all values of x greater then or equal to 6 i.e. [tex]x\geq 6[/tex] . Correct answer is D) 6 less-than-or-equal-to x less-than infinity .

Answer:

the answer is D. 6 ≤ x < ∞

Step-by-step explanation:

the answer is D. 6 ≤ x < ∞