determine where f is continous. if possible extend f to a new function that is continous on a larger domain

Question

1. f(x)=4x/x^2-1
2. x^2 tan x
i really dont understand how to solve these please help

Answer 1

rational functions are continuous except where the denominator is zero, since division by zero is undefined.
So, 4x/(x^2-1) is discontinuous at x=±1

From your precal studies of trig, you know that tanx has asymptotes at all odd multiples of π/2/ So, x^2 tanx is discontinuous there as well.