Question

Which would be the domain in this case?
f(x)=[x+2]/[x^2+7x+10]
I know that we can factorize the denominator like this: (x+2)(x+5).
So the roots of the denominator are -2 and -5.
But I can cancel out x+2 from the numerator....
So the domain is all real - {-2,-5}
OR all real -{-5} ??

Answer 1

The numbers that make the denominator 0 are not included in the domain, so its all real numbers except -2 and -5

Answer 2

I made a oopsy

Answer 3

This is the same as 1/x+5

so domain is all except -5

Answer 4

But we can rewrite f(x) this way:
\[f(x)=\frac{x+2}{x^2+7x+10}=\frac{x+2}{(x+2)(x+5)}=\frac{1}{x+5}\]
Isn't this called a "hole"?
Could you give me a resource to check this?

Answer 5

Yeah thats what i was saying, not sure its called anything, but if you graph it -2 is in the domain

Answer 6

mm.. What about this?
http://www.purplemath.com/modules/grphrtnl4.htm

Answer 7

Thats kinda interesting..

Answer 8

But there it says that we have to consider the roots of the denominator of the original function.
Which is true?