You can put this solution on YOUR website! I believe your problem is to find the domain of:
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The only thing we have to be concerned about in this equation is the quantity inside the
radical sign.
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In the real world that quantity cannot be negative because you can't take the square root
of a negative number. The quantity can be zero or positive only.
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Therefore we can set up this equation:
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and we can solve this equation by first subtracting 21 from both sides of the equation to
eliminate the +21 on the left side. After this subtraction the equation is:
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Finally, to solve for x, just divide both sides by 3 and you get:
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So x = -7 is a critical point. What happens if we let ? The term inside the radical
becomes . Not good because it's negative. But what happens if we let ? The term inside the radical becomes . That's OK!
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From this exercise we can gather that x must be at least -7, but it can be a more positive
value than that. We can write this inequality as:
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and we can say that the domain of x is all real values from and including -7 outward to
positive infinity.
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Hope this gives you a feel for how domain problems such as these can be done. Start by
looking for something that is not mathematically allowed such as square roots of negative
numbers, divisions by zero, or something similar. The find a way to avoid that situation
by defining limits on x.
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