Determine if the following function is continuous: f(x) = (x-iy)/(x-1)
How do find out if a function is continuous without graphing it and without a point to examine? I know I've learned this, probably in pre-calculus too, but I'm blanking
The Attempt at a Solution
u(x) = x-iy as a function is continuous because, due to the i term, x-iy will never equal 0 and it is a linear function
v(x) = x-1 is also continuous,as it is a linear function that exists under all conditions
if u and v are both continuous under all conditions, than u/v must also be continuous?