Finding the Domain of a Function
Date: 9/28/95 at 15:29:13 From: Anonymous Subject: calculus What is the domain of f(x)=((2-x)/(x-2))^.5 ?
Date: 9/28/95 at 17:44:34 From: Doctor Jonathan Subject: Re: calculus Since the square root is only defined to be real over non-negative numbers, the domain of this function is the solution to the inequality: (2-x)/(x-2) >= 0 This will occur when the numerator and the denominator have the same sign, or when the numerator is 0. Well, the numerator in this case is only positive for x > 2, and the denominator is only positive for x < 2. In other words, they have different signs (they are in fact opposite) over all x. So what happens at x = 2? Well, here the denominator ruins things for us by being zero, and so the function is undefined even at x = 2. So, there are no values of x such that f(x) is defined. As such, the domain is the empty set. Hope this helps... -Doctor Jonathan, The Geometry Forum
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