Find vertical tangent lines of . (how do you do square root symbols?)
, x=complex number, so there are no vertical tangent lines?
Edit: Or actually, will never be zero, so the denominator would have to be a root function or a fraction to be a vertical tangent line?
In functions like these, the most common 'cause' of a function being undefined is a divide by zero at for some value of x. Thus, yes, the denominator of such a function must be equal to zero at some value of x.
There are other reasons why a function may be undefined, but in this type of example, you'd need some sort of division by 0, and that does not occur in the real plane for this function.