How can I find the domain of this function?

[letranger9000]

f(x) = (√(1-2x))/(x^2 -9) + 3/(x^2 - 6x +8)


I thought:


x^2-9 -> (x-3)(x+3)


x^2-6x+8 -> (x-4)(x-2)




(√1-2x) (x-4)(x-2) + 3(x-3)(x+3)
---------------------------------------
(x-3)(x+3)(x-4)(x-2)


I just don't know what to do next and it just feels not right , please someone tell me how can I find the domain.

 

[letranger9000]

WHY do you not simply use 1 - 2x

Or do you mean SQRT(1 - 2x)?

My bad, -> SQRT(1 - 2x)

 

[DrPhil]

f(x) = (√1-2x)/(x^2 -9) + 3/(x^2 - 6x +8)


I thought:


x^2-9 -> (x-3)(x+3)


x^2-6x+8 -> (x-4)(x-2)




(√1-2x) (x-4)(x-2) + 3(x-3)(x+3)
---------------------------------------
(x-3)(x+3)(x-4)(x-2)


I just don't know what to do next and it just feels not right , please someone tell me how can I find the domain.

There is nothing wrong with what you have done. Any time there is a zero in a denominator, that point has to be excluded from the domain. I would not think it necessary to combine the two rational expressions over the complete common denominator, since the function is undefined if either term is undefined.

I suspect the term with the radical is supposed to be √(1-2x) rather than √1-(2x). In that case you also need to reject any x that leads to the square root of a negative number.