Question

Find the domain of the following rational functions.

y=(6x-5)/(x^2-6x+4)

I got {XER} but I'm not sure if that's correct.

Answer 1

by domain you just mean whether it's all real numbers or not correct?

Answer 2

Yes, basically whether there are any limitations on the x-values.

Answer 3

note that denominator cannot be = 0
so, exclude those values for which
(x^2-6x+4) =0

Answer 4

I figured that since it cannot be factored, it has no solution, and therefore results in all real numbers. Unless there IS a way to solve it?

Answer 5

even if you use the quadratic formula?

Answer 6

there is a solution, but not rational, irrational roots are there

Answer 7

and you need to exclude those from real domain too

Answer 8

[6+/-\sqrt{20}/2 \]

Answer 9

not sure if the answer would be left in radical form

Answer 10

= \(3\pm \sqrt 5\)

Answer 11

so, you domain will be all real values of x , excluding
x = 3 -sqrt 5 , x = 3 +sqrt 5

Answer 12

But how did it go from \[(6\pm \sqrt{20})\div2\] to 3 +/-sqrt 5

Answer 13

\(\Large \sqrt{20}=\sqrt {5\times4 }=\sqrt 4\sqrt 5=2\sqrt5\)

Answer 14

then cancelling out 2 from numerator and denominator

Answer 15

Ohh, right. Thank you! I remember doing that last year, but we haven't reviewed it again this year.

Answer 16

welcome ^_^