find the value of x at which f is not continuous and whether each such value is a removable discontinuity:
(a) f(x) = abs(x) / x
(b) f(x) = (x^2 + 3x) / (x + 3)
(c) f(x) = (x - 2) / (abs(x) - 2)

Question

find the value of x at which f is not continuous and whether each such value is a removable discontinuity:
(a) f(x) = abs(x) / x 
(b) f(x) = (x^2 + 3x) / (x + 3)
(c) f(x) = (x - 2) / (abs(x) - 2)

anonymous · Answer

in each of these cases, f will fail to be continuous when the denominator is zero, so for (b), f is discontinuous at x=-3. The discontinuity is removable if you can factor things in a way that gets rid of the discontinuity. For example, (b) factors into $$\frac{x(x+3)}{(x+3)} = x$$, so the discontinuity is removable.