SOLUTION: Determine thed omain of {{{f(x) = (x^2-3) / (the_square_root_of_ 2x^3 + 7x^2 - 6x -21)}}}domain From what I learned in class I assumed I was supposed to use scientific division

Algebra ->  Functions -> SOLUTION: Determine thed omain of {{{f(x) = (x^2-3) / (the_square_root_of_ 2x^3 + 7x^2 - 6x -21)}}}domain From what I learned in class I assumed I was supposed to use scientific division      Log On


   



Question 78551: Determine thed omain of f%28x%29+=+%28x%5E2-3%29+%2F+%28the_square_root_of_+2x%5E3+%2B+7x%5E2+-+6x+-21%29domain
From what I learned in class I assumed I was supposed to use scientific division to find all possible zeros but I have no idea what numbers I would plug into that equation.
My deepest thanks for any help you can give, you're all life savers! :]

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Determine thed omain of f%28x%29+=+%28x%5E2-3%29+%2F+%28the_square_root_of_+2x%5E3+%2B+7x%5E2+-+6x+-21%29
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You only need to look at the denominator; Since it is a radical the radicand
must be >=0; but since it is the denominator it cannot be zero.
So it must be 2x^3+7x^2+6x-21>0
Graph to see where it is >0
I get x>1.2083653
That is the domain
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Cheers,
Stan H.