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svetlana [45]
3 years ago
14

Ya'll please help me!!!!. The water was pumped out of a backyard pond, What is the domain of this graph????

Mathematics
2 answers:
saw5 [17]3 years ago
6 0
Stuck on the same question and it looks like nobody cares to answer on this website
OleMash [197]3 years ago
3 0

Answer:

A. Real numbers from 0 to 8.

Step-by-step explanation:

Since, the given graph represents the depth of water pumped out of the backyard pound,

So, time ( in minutes ) must show the input value and depth ( in inches ) must show the output value,

Also, by the given graph,

Time is defined from 0 to 8 minutes,

Thus, the possible input values of the function of the graph are all the real number between 0 to 8,

Now, we know that the set of all possible input values is called domain of the function,

Hence, the domain of the given graph is,

Real numbers from 0 to 8.

Option 'A' is correct.

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\large\begin{array}{l} \left\{\!\begin{array}{l} \mathsf{f(x)=x^2-6x+2}\\ \mathsf{g(x)=\sqrt{x}}\\ \end{array}\right. \end{array}


\large\begin{array}{l} \textsf{a) }\mathsf{(f\circ g)(x)}\\\\ =\mathsf{f\big[g(x)\big]}\\\\ =\mathsf{\big[g(x)\big]^2-6\cdot g(x)+2}\\\\ =\mathsf{\big[\sqrt{x}\big]^2-6\sqrt{x}+2}\\\\\\ \therefore~~\boxed{\begin{array}{c}\mathsf{(f\circ g)(x)=x-6\sqrt{x}+2} \end{array}}\qquad\checkmark \end{array}

______


\large\begin{array}{l} \textsf{b) }\mathsf{(g\circ f)(-2)}\\\\ =\mathsf{g\big[f(-2)\big]}\\\\ =\mathsf{\sqrt{f(-2)}}\\\\ =\mathsf{\sqrt{(-2)^2-6\cdot (-2)+2}}\\\\ =\mathsf{\sqrt{4+12+2}}\\\\ =\mathsf{\sqrt{18}}\\\\ =\mathsf{\sqrt{3^2\cdot 2}}\\\\ =\mathsf{3\sqrt{2}}\\\\\\ \therefore~~\boxed{\begin{array}{c}\mathsf{(g\circ f)(-2)=3\sqrt{2}} \end{array}}\qquad\checkmark \end{array}

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If you're having problems understanding this answer, try seeing it through your browser: brainly.com/question/2181559


\large\textsf{I hope this helps. :-)}


Tags: <em>composite function composition evaluate algebra</em>

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