Quick Math Question

Kato · January 2012

Ok...the only reason I am asking this is because I had to copy the problems from a friend's book because my book should show up sometime next week. Otherwise, I would look through the book to find my answer. Here is the problem:

Find the domain of the function:

5x + 4 / x(squared) + 3x + 2

I don't want anyone to do the problem for me. I just need a little guidance. The domain is basically the x axis. So...is the domain the result of the numerator combined with the result of the denominator? As in...this is a Piece Wise?

P.S. Sorry if that is not coming out right...I don't know how to make the x to the second power show up properly with BBCode. The 5x + 4 is the numerator, rest is the denominator in case it didn't come out right.

Draygo · January 2012

They are asking you what set of numbers x can be:

http://www.freemathhelp.com/domain-range.html

for example if the equasion was 2/x x cannot be 0 as then you would be dividing by zero.

Lord Palington · January 2012

Exactly. All polynomial functions have a domain of all real numbers, but rational functions (which you have there) are trickier.

You know a fraction can't have a denominator of zero, right? Hopefully that's a good starting point.

ED! · January 2012

Kato wrote:

The domain is basically the x axis.

You mean the domain is all real numbers. The x-axis is just one piece of a co-ordinate system, and it could be anything depending on what "variables" we are working with.

So...is the domain the result of the numerator combined with the result of the denominator? As in...this is a Piece Wise?

Not quite; the domain of the rational function is the intersection of the domain of the numerator and the domain of the denominator. In this case you're going to get all reals, since both the num and dom are polynomial functions. Now you need to find which real numbers will make the entire function undefined, and that occurs when you have a zero in the denominator.

The more of these you do you'll start just looking at a function and recognizing where things will go wrong.

tarnok · January 2012

Part of the problem is that conflating "domain" and "x" is the result of a necessary simplification. They are not precisely the same thing. In your case when you are talking about the domain what you mean is the set of all real number which, when substituted for x, produce a real value for the function.

Or to put it another way; they're asking "what are all of the possible numbers that you can put into the expression and get a real number back?"

Demerdar · January 2012

Don't divide by zero or take the square root of a negative number.

Penny Arcade

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