Question

How do you find the domain of the function `f(x)= x/(x^2+2x-3)`?

Answer 1

Don't take even roots of negative numbers. -- No probhem there are no roots at all.

Don't try9 to divide by `0`. There is a division, so we need to make sure that `x^2+2x-3` is not `0`.

OK, so when is it `0`?

Solve `x^2+2x-3 = 0`

`(x+3)(x-1)=0`

`x= -3, 1`

These are the numbers we need to throw out of the domain. So tlhe domain is all real numbers except `-3,1.`

(In interval notation: `(-oo, -3) uu (-3, 1) uu (1,oo)`)