SOLUTION: which of the following expression could be used as a denominator of a rational function without placing any limits on the domain of the function?
a)2x+3
b)\sqrt(x^2+5)
c)x^2-9
Question 1155244: which of the following expression could be used as a denominator of a rational function without placing any limits on the domain of the function?
a)2x+3
b)\sqrt(x^2+5)
c)x^2-9
d)x^2-x-6
e)2,321
f)none Found 3 solutions by MathLover1, greenestamps, ikleyn:Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!
a denominator of a rational function without placing any limits on the domain of the function is a denominator without variable
The -values at which the denominator equals zero are called singularities and are not in the domain of the function.
so, your answer is:
e) Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!
a) 2x+3. No; 2x+3 is 0 when x is -1.5
b) sqrt(x^2+5). Yes! sqrt(x^2+5) is always greater than 0
c) x^2-9. No, x^2-9 is 0 when x is 3 or -3
d) x^2-x-6 = (x-3)(x+2). No, that is 0 when x is 3 or -2
e) 2321. Yes; that is obviously never 0
ANSWERS: b and e
---------------------------------
I stand corrected. I did not know that the definition of rational function required both numerator and denominator to be polynomials. My previous understanding was that a rational function was simply a ratio of two functions....
In my post, I'd like to make correction to the post by @greenestamps.
b) sqrt(x^2+5) CAN NOT be the denominator of a rational function.
Only POLYNOMIAL or a constant term can be.
So, the unique answer to the problem's question is option e) 2321.