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

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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(13198)   (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....


Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.

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.


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