Question

Which statement best describes f(x)= -2 √x-7 +1 –6 is in the domain of f(x) but not in the range of f(x). –6 is not in the domain of f(x) but is in the range of f(x). –6 is in the domain of f(x) and in the range of f(x). –6 is neither in the domain of f(x) nor in the range of f(x).

Answer 1

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, $f(x)=-2\sqrt{x-7}+1$.

So, the domain of the function is obtained when $x-7\geq 0$ i.e. $x\geq 7$

That is, the domain is {x | x≥ 7}.

Now as we have,

$x\geq 7$ → $x-7\geq 0$ → $\sqrt{x-7} \geq 0$ → $-2\sqrt{x-7} \leq 0$ → $-2\sqrt{x-7}+1 \leq 1$.

That is, $f(x)\leq 1$

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).