Answer:
Option B.
Step-by-step explanation:
The given function is
[tex]f(x)=-2\sqrt{x-7}+1[/tex]
The above function is defined if (x-7) is greater than 0.
[tex]x-7\geq 0[/tex]
Add 7 on both sides.
[tex]x\geq 7[/tex]
It is means domain of the function is [tex][7,\infty)[/tex]. So, -6 is not in domain.
We know that
[tex]\sqrt{x-7}\geq 0[/tex]
Multiply both sides by -2. So, the sign of inequality will change.
[tex]-2\sqrt{x-7}\leq 0[/tex]
Add 1 on both sides.
[tex]-2\sqrt{x-7}+1\leq 0+1[/tex]
[tex]f(x)\leq 1[/tex]
It is means range of the function is [tex](-\infty,1][/tex]. So, -6 is in Range.
Since –6 is not in the domain of f(x) but is in the range of f(x), therefore the correct option is B.
