Question

Let f(x)=x^2+6x+8/x^2-11x+10 . What is the domain of f(x)?

Answer 1

set \[x^2-11x+10\neq0\]

Answer 2

You may factor out the denominator to know what are the values that will make it zero...

Answer 3

so its -2, and -4 right?

Answer 4

(x+4)(x+2)
-----------
(x-1)(x-10)

Answer 5

How can you say so? @security4286

Answer 6

what?

Answer 7

Dear Security:
This function f(x) is a RATIONAL FUNCTION. As our friends Sour and Lilie have already hinted, rational functions are defined for all x EXCEPT those for which the denominator is zero. Are you concentrating on the denominator? -2 and -4 are roots of the numerator.

Answer 8

Complete the following:

"The domain of the given rational function is

(-infinity, ) U ( , ) U ( , infinity)."

Answer 9

Roots of the denominator, not the numerator @security4286

Answer 10

I'll post this again:

(x+4)(x+2)
------------
(x-1)(x-10)

x-1 /= 0
x-10 /= 0

solve for x

Answer 11

You may also write
\[D = \mathbb{R} \left\{ ? \right\}\]

Answer 12

Security: Your helpers need the security of knowing that you're still with us in this problem solution. Are you?

Answer 13

yah dude i already got my answer it was x=1 and x=10

Answer 14

something like all are real numbers except x=1 and x=10, idk if my wording is that accurate but yah i got what i needed thank you all :D