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Question 484117: what is the domain and range of the function... f(x)= square root of (9-x^2)/ x+2
Answer by chessace(471)   (Show Source):
You can put this solution on YOUR website! Domain: It will the whole real line except parts that ruin the formula.
First look at the denominator: x = -2 will cause a division by 0, so it is out.
Next look at the square root: x < -3 or x > 3 will cause square root function to operate on a negative, that's not real.
So Domain is 2 intervals: (a) [-3, -2) i.e. x >= -3 and x < -2, and (b) (-2, 3] i.e., x >-2 and x <= 3.
To find the range, look at the end points of the interval and what generally happens within.
When x = -3, f = 0. As x increases, f is negative (positive / negative) and without limit as x approaches -2. Similarly, f(3) = 0 and goes positive as x deceases, again without limit as it approaches -2.
So the range is the whole real line (y axis).
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