Respuesta :
Answer:
B. -6 does not belong to the domain but belongs to the range of f(x).
Step-by-step explanation:
We have the function, [tex]f(x)=-2\sqrt{x-7}+1[/tex].
So, the domain of the function is obtained when [tex]x-7\geq 0[/tex] i.e. [tex]x\geq 7[/tex]
That is, the domain is {x | x≥ 7}.
Now as we have,
[tex]x\geq 7[/tex] → [tex]x-7\geq 0[/tex] → [tex]\sqrt{x-7} \geq 0[/tex] → [tex]-2\sqrt{x-7} \leq 0[/tex] → [tex]-2\sqrt{x-7}+1 \leq 1[/tex].
That is, [tex]f(x)\leq 1[/tex]
Thus, the range of the function f(x) is {y | y≤ 1}.
Thus, we can see that,
-6 does not belong to the domain but belongs to the range of f(x).
