Answer:
-6 is not domain of f(x) but is in range of f(x)
B is correct.
Step-by-step explanation:
Given: [tex]f(x)=-2\sqrt{x-7}+1[/tex]
Domain is input value of x where function is well defined.
Range is output value of f(x) for defined value of x.
Here, we have square function. As we know the value inside the square must be positive.
Therefore, x-7≥0
x≥7
Domain: x≥7 or [7,∞)
For range, we will put x=7 into function.
[tex]f(7)<-2\sqrt{7-7}+1[/tex]
[tex]f(7)<0+1[/tex]
[tex]f(7)<1[/tex]
The maximum value of f(x) is 1.
Range: f(x)<1 or (-∞,1)
-6 is not belongs to domain.
-6 is belongs to range.
Hence, -6 is not domain of f(x) but is in range of f(x)
