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Find the domain and rainge of this function (rational fn)

  • Thread starter skyturnred
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Homework Statement



Find domain and range of

f(x,y)=[itex]\frac{-3y}{x^{2}+y^{2}+1}[/itex]

Homework Equations





The Attempt at a Solution



It's quite obvious the the domain is R[itex]^{2}[/itex], because there are no possible values of x or y that would make the denominator 0.

But as for the range, my prof said that the range is from -3/2 to 3/2.

I can't figure out why. In my opinion, the range should be R[itex]^{3}[/itex], shouldn't it? I mean, there is no value y that would make the function not make sense. Also, x isn't even in the numerator and since we already accounted for it in the denominator, there is also no value x that would make the function not make sense. So how isn't the range R[itex]^{3}[/itex]?

Thanks in advance for the help.
 

Answers and Replies

  • #2
7
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The range isn't R^3 because the function f: R^2->R^1.
 

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