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Neko [114]
3 years ago
10

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 domai

n 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).
Mathematics
1 answer:
Archy [21]3 years ago
5 0

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).

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The answer to the question: "Will Hank have the pool drained in time?" is:

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Now we know Hank has 360 minutes to drain the pool, we're gonna calculate the volume of the pool with the given measurements and the next equation:

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Since the drain rate is in gallons, we must convert the obtained volume to gallons too, we must know that:

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  • <u>Time to drain the pool ≅ 326 minutes</u> (I approximate to the next number because I want to assure the pool is drained in that time)

As we know, <u><em>Hank has 360 minutes to drain the pool and how it would be drained in 326 minutes approximately, we know Hank will have the pool drained in time and will have and additional 34 minutes</em></u>.

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