steps to find the range of function with two variables

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• October 15th 2012, 01:48 PM
nursyafika
steps to find the range of function with two variables
hi everyone!
i need your opinion on how to find range of function.
eg: f(x,y)=x2+y2-1
(Happy)thanks for all your responses!
• October 15th 2012, 02:04 PM
TheEmptySet
Re: steps to find the range of function with two variables
Quote:

Originally Posted by nursyafika
hi everyone!
i need your opinion on how to find range of function.
eg: f(x,y)=x2+y2-1
(Happy)thanks for all your responses!

If we square something we know that it will always be nonegative!

This gives

$x^2 \ge 0$ and $y^2 \ge 0$

So the smallest that the function can be is....

$f(x,y)=x^2+y^2-1 \ge 0+0-1=-1$

Can you finish from here?