Finding the Domain of a FunctionDate: 02/10/2009 at 11:14:05 From: Brandon Subject: Domain of a function I'm having trouble finding the domain of a function. I'm trying to do all of this on an online math class and its just extremely hard to understand all of it by reading it off a web page instead of having it taught in front of me. Date: 02/10/2009 at 14:19:00 From: Doctor Ian Subject: Re: Domain of a function Hi Brandon, One thing that works for me is to actually read my textbook (or a web page, or any other written resource) out loud, word by word... as if someone else is reading it to me. You'd be surprised at how much this can help you, if only because it keeps you from skimming past a few words here and there that turn out to be critically important. (By the way, if you're planning to go to college, learning to teach yourself from written resources is a skill that you need to be polishing. When you're in college, classes aren't where the teacher reads the book to you, as in high school. Classes are where the professor discusses material that he assumes you've already read before class.) Anyway, the domain of a function is the set of legal inputs. Given a function like f(x) = 2x we can put in any real number for x, and get a sensible value for the function. So the domain is "all real numbers". Contrast that with __ f(x) = \/ x Now we get nonsense if we put in a negative value of x, but we're okay with any other real numbers. So the domain is "all non-negative real numbers" or "all real numbers greater than or equal to 0". We can change that slightly, so it looks like ______ f(x) = \/ x - 3 and now it works as long as x is not less than 3. So the domain becomes "all real numbers not less than 3" or "all real numbers greater than or equal to 3". Dividing by zero is another no-no, so we might write a function as ______ f(x) = 1 / \/ x - 3 Now we can't use 3, either, because it would require us to divide by zero. So the domain becomes "all real numbers greater than 3". What about something like f(x) = 1 / [(x + 1)(x - 2)] ? Now we're fine except if x is -1, or 2. So the domain is "all real numbers except -1 or 2". And so on, and so on. Basically, the idea is that you look at your function, and you consider what values might cause it to "break", by requiring you to take the square root of a negative number, or divide by zero, or get a value of sin(x) greater than 1, or anything else that doesn't make sense. And you remove those values from the set of real numbers. What remains, is your domain. Does that make sense? If not, try reading it out loud. And if it still doesn't make sense, write back and let me know which sentence starts to lose you, okay? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ Date: 02/10/2009 at 18:51:30 From: Brandon Subject: Thank you (Domain of a function) Thank you for the help! I understand better now. You were very thorough and easy to understand, which is a big help. Thanks again. And I may be back! |
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