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Question 638423: How would I find the domain of y = 3rd root (x - 6) / square root (x^2 - x - 30) ?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! find the domain of y = 3rd root (x - 6) / square root (x^2 - x - 30) ?
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y = (cbrt(x-6))/(sqrt[(x-6)(x+5)]
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The denominator cannot be zero and (x-6)(x+5) cannot be negative.
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Solve (x-6)(x+5) > 0
Draw a number line.
Plot x = -5 and x = 6
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Find the solution interval for x-values.
If x < -5 the product is > 0
If -5< x <6 the product is < 0
If x > 6 the product is > 0
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So the domain is All Real Numbers in (-oo,-5)U(6,+oo)
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Cheers,
Stan H.
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