The functions f and g defined by fx x3 3x2 2x2 1 and gx

The functions f and g defined by f(x) = x^3 - 3x^2 + 2/x^2 - 1 and g(x) = x^2 + 4x - 5/x^3 - 2x^2 + x are each undefined at two points. Determine whether or not the discontinuities at those points are removable.

Solution

f(x) is discontinuous at x=1.

g(x) is discontiuous at x=1.

f(x) is continuous with f(1)=0,g(x) is continous with g(1)=6.