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 1.Please explain me with an example h...
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Sun September 09, 2012 By: R.k. Kumar
1.Please explain me with an example how to find Domain & Range.
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The domain is the values of x that can be put into the equation, and will return a yvalue. The range is all the values of y that will come out given the domain.
So if you look at simple one, y = x^2. There is no x=value you can't put in, so the range is R (all real numbers). Since it is x^2, no matter what you put in, a positive number will return, and 0 x will return 0 y. So the range is R+ u 0 (all real numbers, in union with zero).
If you look at y = 1/x, there is a restriction in the domain. You can't have x = 0, because you can't divide by zero. Other than this, all xvalues will return a yvalue (as opposed to 'undefined'). So the range is R\{0} (or, all real numbers, not including zero). As xapproached 0, y becomes very large, and as x becomes large, ybecomes small. However, nothing you put in will result in y being equal to zero. So the range is also y = R\{0}.
So if you look at simple one, y = x^2. There is no x=value you can't put in, so the range is R (all real numbers). Since it is x^2, no matter what you put in, a positive number will return, and 0 x will return 0 y. So the range is R+ u 0 (all real numbers, in union with zero).
If you look at y = 1/x, there is a restriction in the domain. You can't have x = 0, because you can't divide by zero. Other than this, all xvalues will return a yvalue (as opposed to 'undefined'). So the range is R\{0} (or, all real numbers, not including zero). As xapproached 0, y becomes very large, and as x becomes large, ybecomes small. However, nothing you put in will result in y being equal to zero. So the range is also y = R\{0}.
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