in 1/x2+y , is this expression defined when y is positive

Question

I dont know this. another question on that equation, is that defined when y is negative?

 

Answer 1

I assume the expression is 1/(x²+y).  In math division by zero is undefined.  So when you have a rational expression like this, the expression will be undefined when the denominator is zero.  The denominator is (x²+y), so we need to know the values of x and y that can make it equal to zero.

 

There are two terms in the denominator, x² and y.  x² will always be positive, even if x is negative ((-2)² = (-2)*(-2)=4).  So if y is also positive, the denominator cannot equal zero.  Hence 1/(x²+y) is defined for y>0.

 

When y is negative (y<0), then the denominator can be zero.

 

     x²+y = 0

     y = -x²

 

For example, suppose x=2 and y = -4:

 

     x²+y = 2²-4 = 4-4 = 0. 

 

So 1/(x²+y) will be undefined whenever y = -x².