Answer:
-6 is not in the domain of f(x) but in the range of f(x)
Step-by-step explanation:
I think your question is missed of key information, allow me to add in and hope it will fit the original one. Please have a look at the attached photo.
My answer:
The given function is:
f(x) = -2[tex]\sqrt{x-7}[/tex] + 1
To make f(x) is defined, the value inside the square root must be ≥0
<=> x - 7 ≥0
<=> x ≥7
=> -6 is not in the domain of f(x)
How about in the range of f(x)? We can test it by using this ex:
f(x) = -2[tex]\sqrt{x-7}[/tex] + 1 = -6
<=> -2[tex]\sqrt{x-7}[/tex] = -7
<=> [tex]\sqrt{x-7}[/tex] = 7/2
<=> x - 7 = 49/4
<=> x = 77/4 ≥7
So -6 is in the domain of f(x)
–6 is not in the domain of f(x) but is in the range of f(x)
