Respuesta :
Option B shows the correct representation of the given function.
Option B is "–6 is not in the domain of f(x) but is in the range of f(x)."
Function
A Function can be defined as an expression that defines a relationship between one independent variable with another dependent variable.
The given function is [tex]f(x) = -2\sqrt{x-7} +1[/tex].
Let us consider that x-7 is greater than or equal to 0. Then,
[tex]x-7 \geq 0[/tex]
[tex]x\geq 7[/tex]
The value of x greater than or equal to 7 shows the domain function. Hence the domain function is [tex](7, \infty)[/tex].
Now if x-7 is greater than or equal to 0 then,
[tex]\sqrt{x-7} \geq 0[/tex]
If the above equation is multiplied by -2 then,
[tex]-2\sqrt{x-7} \leq 0[/tex]
Now add +1 in both sides of the above equation, we get,
[tex]-2\sqrt{x-7} + 1\leq 1[/tex]
[tex]f(x)\leq 1[/tex].
The above expression of the function represents that the given function is in the range of [tex](-\infty , 1)[/tex].
Hence we can conclude that option B represents the correct expression that is "–6 is not in the domain of f(x) but is in the range of f(x)".
To know more about the function, follow the link given below.
https://brainly.com/question/5245372.
